UC-NRLF 


71    227 


Theory  of  Development 


By  A*  a  NIETZ 


Monographs  on  the  Theory 
of  Photography,  from  the 
Research  Laboratory  of  the 
Eastman  Kodak  Company. 

No.  2 


Monographs  on  the  Theory  of  Photography  from  the 
Research  Laboratory  of  the  Eastman  Kodak  Co. 

No.  2 


COPYRIGHT  1922 
EASTMAN  KODAK  COMPANY 


The  Theory  of  Development 


By  A.  H.  Nietz 


ILLUSTRATED 


D.  VAN  NOSTRAND  COMPANY 
NEW  YORK 

EASTMAN  KODAK  COMPANY 
ROCHESTER,  N.  Y. 

1922 


MONOGEAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Edited  by 
C.  E.  KENNETH  MEES 

and 
MILDRED  SPARGO  SCHRAMM 


Monographs  on  the  Theory 
of  Photography 

No.  1.     THE  SILVER   BROMIDE   GRAIN   OF  PHOTOGRAPHIC 
EMULSIONS.     By  A.  P.  H.  Trivelli  and  S.  E.  Sheppard. 

No.  2.     THE  THEORY  or  DEVELOPMENT.     By  A.  H.  Nietz. 

No.  3.     GELATIN  IN  PHOTOGRAPHY.     Volume  I.      By  S.  E. 
Sheppard,  D.  Sc. 

Price  each  $2.50 


Other  volumes  soon  to  appear: 
AERIAL  HAZE  AND  ITS  EFFECT  ON  PHOTOGRAPHY  FROM  THE  AIR 

THE  PHYSICS  OF  THE  DEVELOPED  PHOTOGRAPHIC  IMAGE. 
By  F.  E.  Ross,  Ph.  D. 

GELATIN  IN  PHOTOGRAPHY.    Volume  II.    By  S.  E.  Sheppard, 
D.  Sc. 


533241 


Preface  to  the  Series 

The  Research  Laboratory  of  the  Eastman  Kodak  Company 
was  founded  in  1913  to  carry  out  research  on  photography 
and  on  the  processes  of  photographic  manufacture. 

The  scientific  results  obtained  in  the  Laboratory  are 
published  in  various  scientific  and  technical  journals,  but  the 
work  on  the  theory  of  photography  is  of  so  general  a  nature 
and  occupies  so  large  a  part  of  the  field  that  it  has  been 
thought  wise  to  prepare  a  series  of  monographs,  of  which  this 
volume  is  the  second.  In  the  course  of  the  series  it  is  hoped 
to  cover  the  entire  field  of  scientific  photography,  and  thus 
to  make  available  to  the  general  public  material  which  at  the 
present  time  is  distributed  throughout  a  wide  range  of  journals. 
Each  monograph  is  intended  to  be  complete  in  itself  and  to 
cover  not  only  the  work  done  in  the  Laboratory,  but  also  that 
available  in  the  literature  of  the  subject. 

A  very  large  portion  of  the  material  in  these  monographs 
will  naturally  be  original  work  which  has  not  been  published 
previously,  and  it  does  not  necessarily  follow  that  all  the 
views  expressed  by  each  author  of  a  monograph  are  shared 
by  other  scientific  workers  in  the  Laboratory.  The  mono- 
graphs are  written  by  specialists  qualified  for  the  task,  and 
they  are  given  a  wide  discretion  as  to  the  expression  of 
their  own  opinions,  each  monograph,  however,  being  edited 
by  the  Director  of  the  Laboratory  and  by  Mrs.  Schramm,who 
is  the  active  editor  of  the  series. 


Rochester,  New  York 
October,  1922 


Preface 

The  present  monograph  presents  the  results  of  investigations 
undertaken  to  determine  the  reduction  potentials  of  certain 
organic  developers,  and  to  establish  the  connection  between 
these  potentials  and  the  developing  characteristics  of  the 
various  compounds.  It  was  originally  intended  to  use  both 
electrometric  and  photographic  methods,  but  since  the  results 
obtained  by  the  latter  method  are  complete,  it  has  been  de- 
cided to  publish  these  at  the  present  time. 

In  the  course  of  the  work  a  large  amount  of  sensitometric 
data  has  been  accumulated,  as  well  as  much  information  rela- 
tive to  various  other  aspects  of  the  process  of  development. 
The  inclusion  of  what  may  seem  an  unwarrantedly  large 
amount  of  these  data  seems  justified  by  the  desire  to  render 
the  information  obtained  as  useful  as  possible  for  future  work 
as  well  as  to  support  the  various  conclusions  reached. 

The  results  here  presented  should  normally  have  been  pub- 
lished in  a  series  of  papers,  but  this  was  prevented  by  the 
interruption  caused  by  the  war,  and  though  completed  in  1919 
most  of  the  material  is  thus  published  here  for  the  first  time. 

The  author  is  indebted  especially  to  Dr.  W.  F.  Colby  of 
the  University  of  Michigan,  who,  during  the  year  in  which 
he  was  associated  with  this  laboratory,  made  many  valuable 
suggestions  as  to  some  of  the  conceptions  and  methods  of 
interpretation  employed.  Acknowledgment  is  due  also  to 
Mr.  Kenneth  Huse,  who  supervised  the  experimental  work 
for  a  time. 


Rochester,  New  York 
October,  1922. 


The  Theory  of  Development 


CONTENTS 


PREFACE 
CHAPTER 


I.  Developing  Agents  in  Relation  to  their 
Relative      Reduction      Potentials      and 

Photographic  Properties 

General  Introduction. — The  Chemical 
Structure  of  Developing  Agents  and 
its  Relation  to  Photographic  Prop- 
erties. Substances  Investigated. 
Chemical  Theory  of  Reduction  Potential 
Method. — Details  of  Experimental  Work. 
— Sensitometric  Theory. 

CHAPTER  II.  Developing  Agents  in  Relation  to  their 
Relative  Reduction  Potentials  and 
Photographic  Properties  (Continued)  .  . 
Normal  Development  and  the  General 
Effect  of  Bromide  on  Plate  Curves. — 
Experimental  Proof  of  the  Existence  of 
the  Common  Intersection. — Experiments 
Relating  to  the  Effect  of  Bromide  on  the 
Intersection  Point. — Method  of  Evalu- 
ating the  Density  Depression. — Relation 
of  the  Density  Depression  to  Bromide 
Concentration;  Depressions  in  Different 
Developers. 

CHAPTER  III.  Developing  Agents  in  Relation  to  their 
Relative  Reduction  Potentials  and 
Photographic  Properties  (Continued)  .  . 
The  Relations  for  the  Slope  of  the 
Density  Depression  Curves. — The  Varia- 
tion of  C0  with  the  Emulsion  Used.— 
The  Variation  of  C0  with  the  Developer; 
Reduction  Potential  Values. — Previous 
Results  on  Reduction  Potentials. — An 
Energy  Scale  of  Developers. 


Page 

7 


13 


39 


52 


CHAPTER  IV.  A  Method  of  Determining  the  Speed  of 
Emulsions  and  Some  Factors  Influencing 

Speed 59 

Importance  of  the  Method  of  Exposure. 
— Definitions  and  Sensitometric  Concep- 
tions Involved. — A  New  View  of  the 
Matter. — Experimental  Data. 

CHAPTER  V.  Velocity  of  Development,  the  Velocity 
Equation,  and  Methods  of  Evaluating 
the  Velocity  and  Equilibrium  Constants  .  76 
Previous  Work. — Experimental  Methods. 
— Interpretation  of  Results;  Various 
Velocity  Equations  and  Experimental 
Data. — Conclusions  as  to  the  Form  of 
Equation  Best  Expressing  the  Course 
of  the  Reaction. 

CHAPTER  VI.  Velocity  of  Development  (Continued). 
Maximum  Density  and  Maximum  Con- 
trast and  their  Relation  to  Reduction 
Potential  and  to  Other  Properties  of  a 

Developer 97 

The  Velocity  Equation  and  its  Character- 
istics.— Note  on  Experimental  Details. 
—Variation  of  Maximum  Density  with 
Exposure. — Maximum  Contrast  (7o>) 
and  a  New  Method  for  its  Determination. 
— Variation  of  Dm  and  7oo  with  the 
Developer. — The  Latent  Image  Curve. 

CHAPTER  VII.  Velocity  of  Development  (Continued). 
The  Effect  of  Soluble  Bromides  on 
Velocity  Curves,  and  a  Third  Method 
of  Estimating  the  Relative  Reduction 

Potential 112 

The  General  Effect  of  Bromides  on 
Velocity  and  on  Velocity  Curves.— 
Variation  of  Dm  with  Bromide  Concen- 
tration.— A  Third  Method  for  Estimating 
the  Relative  Reduction  Potential.— 
Effect  of  Bromide  on  D  oo  • — Proof  that 
the  Density  Depression  Measures  the 
Shift  of  the  Equilibrium. — Effect  of 
Bromide  on  K. — Variation  of  /0  and 
/a  with  Bromide  Concentration. — The 
Depression  of  the  Velocity  Curves. 


CHAPTER  VIII.  The  Fogging  Power  of   Developers  and 

the  Distribution  of  Fog  over  the  Image    .    134 
The  Nature  of  Fog. — Fogging  Power.— 
The  Distribution  of  Fog  over  the  Image. 
— The  Fogging  Action  of  Thiocarbamide 

CHAPTER     IX.  Data  Bearing  on  Chemical  and  Physical 

Phenomena  Occurring  in  Development    .    157 
The  Effect  of  Neutral  Salts.— The  Effect 
of  Changes  in  the  Constitution  of  the 
Developing  Solution. 

CHAPTER  X.  General  Summary  of  the  Investigation, 
with  Notes  on  Reduction  Potential  in 
its  Relation  to  Structure,  etc 160 


The  Theory  of  Development 


CHAPTER  I 

Developing  Agents  in  Relation  to  their  Relative 

Reduction  Potentials  and  Photographic 

Properties 

GENERAL    INTRODUCTION 

Many  of  the  principles  relating  to  the  chemistry  of  develop- 
ment and  developers  have  been  so  well  established  that  it  is 
unnecessary  to  reiterate  them,  except  in  so  far  as  they  are 
required  to  make  clear  the  purposes  of  the  present  work.  In 
some  cases,  however,  quantitative  measurements  have  been 
urgently  needed,  as  for  instance  in  regard  to  the  effect  of 
soluble  bromides  on  the  development  process,  which  repre- 
sents the  principal  portion  of  the  subject  matter  here. 

Chemically,  photographic  development  is  now  understood 
to  be  a  reduction  process.  Many  of  the  features  of  its  mechan- 
ism, however,  are  relatively  unknown,  as,  for  example,  the 
differentiation  by  certain  reducing  agents  between  the  silver 
halide  which  has  been  affected  by  light  and  that  which  has  not. 
To  clear  up  these  matters  and  to  determine  the  nature  of  the 
latent  image  will  require  extensive  experimental  work  on 
details  which  at  first  seem  to  have  little  bearing  on  the  subject. 
Although  it  is  impossible  at  present  to  rate  the  various  phases 
of  possible  investigation  according  to  their  importance,  it  is 
evident  that  all  effects  of  development  must  be  eliminated  one 
by  one.  The  study  of  development  characteristics  and  of  the 
reduction  potentials  of  developers  is  thus  of  the  greatest 
importance. 

Photographic  development  may  be  divided  into :  (a)  physic- 
al, where  the  silver  forming  the  image  is  supplied  by  the 
developer,  and  on  reduction  is  deposited  on  nuclei  formed  by 
light  action;  (b)  chemical,  where  the  silver  is  furnished  en- 
tirely by  the  silver  halide  of  the  emulsion  and  largely  by  that 
portion  affected  by  light;  and  (c)  a  combination  of  the  two,  in 
which  some  chemical  development  takes  place,  but,  owing  to 
the  solvent  action  of  the  developer,  some  of  the  silver  halide  of 

13 


MONOGRAPHS  ON  THE  THEORY  OP  PHOTOGRAPHY 

the  emulsion  goes  into  solution  from  which  it  is  deposited  on 
nuclei  or  grains  of  silver  already  in  the  emulsion.  It  is  prob- 
able that  most  cases  of  ordinary  alkaline  development  rep- 
resent the  third  class,  though  the  proportion  of  physical 
development  is  usually  small,  perhaps  so  small  that  the  process 
may  be  considered  as  belonging  to  the  second  class.  Physical 
development  is  not  considered  in  the  present  work. 

The  influence  exerted  by  the  developer  in  conditioning  the 
character  and  extent  of  development  has  caused  numerous 
controversies,  most  of  which  could  have  been  avoided  if  data 
on  developers  which  cover  a  wide  range  had  been  available. 
Many  of  the  common  developers  are  much  alike,  and  fall 
.within  very  narrow  limits  on  a  comparative  scale;  but  it 
should  be  remembered  that  a  wide  range  of  characteristics  is 
included  in  the  term  developer. 

Developing  agents  may  be  classified  as  follows : 

(a)  Developers  of  too  low  reducing  energy  to  be  practically 
useful, — e.  g.,  ferrous  citrate; 

(b)  Developers  giving  undesirable  reaction  products, — e.  g., 
hydroxylamine,  hydrazine; 

(c)  Developers    too    powerful    for    practical    use, — e.    g., 
triaminophenol ; 

(d)  Developers  of  practical  utility, — e.  g.,  paraminophenol, 
etc. 

Eder1  divides  developers  into  three  groups: 

1.  Those  which  develop  a  definite  quantity  of  the  latent 
image  before  fogging  sets  in.     (Common  developers) ; 

2.  Those  which  develop  quite  energetically  with  a  minimum 
of  alkali,  but  at  the  same  time  cause  fog; 

3.  Those  which  with  a  maximum  quantity  of  strong  alkali 
scarcely   develop    the  latent   image,  but  develop  fog  vigor- 
ously,—  e.   g.,   phenylhydrazine,  paraphenylenediamine  sul- 
phonic  acid. 

It  is  evident  that  the  common  developers  occupy  similar 
positions  in  these  classifications,  and  are  likely  to  have  many 
properties  in  common, — i.  e.,  those  characteristics  which  make 
them  good  developers.  Therefore,  when  investigating  the 
effects  of  developers,  it  is  necessary  to  go  somewhat  outside 
this  range  or  to  obtain  a  very  high  degree  of  precision  in  the 
measurements  made. 

It  is  obvious  also  that  a  number  of  physical  and  chemical 
characteristics  other  than  the  relative  energy  of  the  compound 
determine  whether  or  not  it  is  a  good  developer. 

1  Eder,  J.  M.,  Ausfuhrliches  Handbuch  fur  Photographic,  Fifth  Edition,  1903,  pp. 
288  et  seq. 

14 


THE  THEORY  OF  DEVELOPMENT 

Useful  criteria  for  developers,  apart  from  such  practical 
considerations,  are: 

1.  Reducing  power  (valency); 

2.  Reduction  potential; 

3.  Velocity  (velocity  function  and  magnitude); 

4.  Temperature  coefficient  of  velocity. 

All  these  are  related  to  the  photographic  properties  of  the 
various  substances  and  furnish  not  only  a  basis  for  quantita- 
tive chemical  measurement  but  also  the  connecting  link  between 
such  measurements  and  those  of  ordinary  photographic 
properties.  The  second  and  third  of  these  criteria  were 
selected  for  investigation. 

The  reduction  potential  of  a  developer,  in  the  sense  in  which 
the  term  is  used  here,  is  a  practical  measure  of  the  reducing 
energy  of  the  developer. 

Bredig,  Bancroft  Nernst,  and  Ostwald  (l)  have  pointed  out 
the  importance  of  the  reduction  potential  in  reactions  in- 
volving chemical  reduction,  and  its  analogy  to  Ohm's  law; 
Velocity  =  Resistance'  ^n  accordance  with  this  analogy,  if  we 
allow  two  developers  to  act  against  various  additional  chemical 
resistances,  such  as  different  concentrations  of  bromide,  the 
resistances  which  cause  the  same  change  in  the  amount  of 
work  done  by  the  developers  should  be  a  measure  of  their 
relative  potentials.  Whether  the  'reduction  potential  thus 
measured  is  identical  with  the  true  electrochemical  potential 
is  a  question  which  cannot  be  settled  with  the  information 
now  available;  it  is  certainly  related  to  it. 

When  applied  to  photographic  development,  the  analogy  to 
Ohm's  law  given  above  may  be  written  in  the  form. 

W     ,         --.  T!    +    ^2    +    ^3 

Velocity  = 


R1+R2+R3     

where  TTI  represents  the  reduction  potential  of  the  developer 
and  is  no  doubt  the  largest  term  of  the  numerator.  The 
other  terms  in  the  numerator  correspond  to  oxidation  poten- 
tials for  the  latent  image  nuclei,  a  sufficiently  high  oxidation 
potential  being  required  (under  fixed  conditions)  to  cause 
reduction,  and  it  being  conceivable  that  different  groups  of 
nuclei  possess  different  oxidation  potentials.  Possibly  other 
factors  are  included.  Undoubtedly  the  reaction  resistance 
represented  by  the  denominator  also  consists  of  several  factors 
or  several  terms.  Thus  it  is  difficult  to  connect  the  velocity 
of  development  with  the  reduction  potential  of  the  developer 

1  For  Citations,  see  bibliography  appended. 

15 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

in  all  cases,  as  the  other  factors  can  not  be  measured  by  present 
methods.  Only  when  some  of  these  factors  can  reasonably 
be  assumed  to  remain  constant  can  two  developers  be  com- 
pared by  this  method.  The  velocity  of  development  is 
affected  by  diffusion  processes  to  such  an  extent  that  any 
factor  influencing  the  latter  changes  the  velocity,  although 
the  potential  may  have  undergone  practically  no  change. 

THE    STRUCTURE    OF    REDUCING    AGENTS    AND    ITS    RELATION    TO 
PHOTOGRAPHIC    PROPERTIES 

Before  discussing  the  methods  of  measurement  and  the 
results  obtained,  it  is  desirable  to  review  the  structure  of 
those  organic  compounds  which  have  been  found  to  develop, 
giving  some  attention  to  the  photographic  properties  said  to  be 
associated  with  them. 

The  brothers  Lumiere  with  Seyewetz,  and,  independently, 
Andresen,  are  responsible  for  much  of  our  knowledge  of  the 
developing  properties  of  various  organic  reducing  agents. 
While  other  authors  have  contributed  to  some  extent,  the 
many  papers  of  Lumiere  and  Andresen  during  the  past  thirty 
years  have  established  general  rules  for  the  structure  of  com- 
pounds which  have  developing  properties.  As  is  now  well 
known,  the  presence  of  hydroxyl  or  amino  groups  or  both  is 
generally  essential  to  developers.  The  following  summary 
of  their  rules  is  taken  from  the  various  papers  of  Lumiere 
and  Andresen.1 

Compounds  in  which  the  developing  function  is  contained 
but  once.  (Two  active  groups.) 

1.  These  comprise  developing  substances  which  contain  in 
one  benzene  nucleus  at  least  two   —OH  groups  or  two   —  NH2 
groups,  or  one  -OH  and  one  -NH2  group; 

2.  These  substances  develop  only  if  the  groups  are  in  the 
para-  or  ortho-  positions.     The  meta-  compounds  have  not 
been  found  to  develop,  so  far  as  known; 

3.  Developers  having  the  two  groups  in  the  para-  position 
are  more  powerful  than  those  in  which  the  groups  are  in  the 
ortho-  position; 

4.  The     dioxybenzenes     are     more     powerful     than     the 
aminophenols,   which    in    turn   are   more   powerful    than    the 
diaminobenzenes ; 

5.  The  developing  properties  are  not  injured  by  the  presence 
of  more  amino  or  hydroxyl  groups; 

1  See  Bibliography. 

16 


THE  THEORY  OF  DEVELOPMENT 

6.  In  the  naphthalene  series  it  is  not  necessary  that  both 
groups  be  attached  to  the  same  benzene  nucleus.     The  general 
rules  governing  developing  function  do  not  apply  to  compounds 
of  this  series; 

7.  Substitution  in  the  amino  or  hydroxyl  groups  disturbs 
the  developing  properties  when  at  least  two  such  groups  in  the 
molecule   do   not   remain    intact.     (Andresen   disagrees  with 
this,  finding  some  cases  where  the  developing  properties  are 
destroyed  by  such  substitutions  and  others  where  they  are 
unchanged  or  even  increased.) 

It  has  been  stated  that  alkyl  substitution  in  the  amino- 
group  increases  the  developing  energy.  Apparently  substi- 
tution for  the  hydrogen  of  the  hydroxyl  group  lowers  the 
developing  energy  or  destroys  the  developing  properties 
altogether; 

8.  Substitution   of   acid   groups    (COOH,   SO3H,   etc.)    for 
hydrogen  in  the  benzene  nucleus  lowers  the  energy; 

9.  Substitution    of   chlorine   or   bromine    for   hydrogen    in 
the  benzene  nucleus  increases  the  developing  energy; 

10.  With  two  hydroxyl  groups  only,  alkali  is  needed; 

11.  With  two  amino  groups  only,  or  with  one    -OH  and 
one  —  NH2  group  the  developer  functions  without  alkali. 

Compounds  in  which  the  developing  function  is  contained 
more  than  once  (three  or  more  active  groups). 

12.  Substances  of  the  benzene  series  containing  three  active 
groups  in  symmetrical  arrangement  (1,  3,  5)  have  no  develop- 
ing power.     The  other  groupings  differ  in  energy,  no  definite 
rule  being  established ; 

13.  The    hydroxy-phenols    which    contain    the    developing 
function  twice  (three  -OH  groups)  can  develop  without  alkali 
but  are  not  practical  when  so  used ; 

14.  If  the  reducing  agent  contains  a  mixture  of   three  or 
more     —OH    and     —  NH2   groups    the    developing   energy   is 
greater  without  alkali  than  it  is  with  alkali  when  the  developing 
function  exists  singly. 

Increasing  the  number  of  amino  groups  greatly  increases 
the  energy; 

15.  In  substances  like  substituted  diphenyl  the  developing 
energy  is  not  increased  by  the  introduction  of  a  third  group 
in  the  second  nucleus; 

16.  In   the  naphthalene  series  the  introduction  of  a  third 
group  raises  the  developing  energy,  regardless  of  the  nucleus 
to  which  it  is  joined. 

17 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

General  effects  of  substitution  in  a  benzene  compound  already 
a  developer.1  (Two  active  groups.) 

(a)  Substitution  of  a  halogen  for  hydrogen  of  the  benzene 
nucleus  in  a  para-  or  ortho-  hydroxy-  or  amino-phenol  raises 
the  energy.     (The  same  substitution  in  the  meta-  compounds 
has  no  effect  on  their  inactivity) ; 

(b)  Substitution  of  an  alkyl  group  in  the  nucleus  has  no 
effect  on  the  developing  energy; 

(c)  Substitution  of  acid  groups  in  the  nucleus  lowers  the 
energy; 

(d)  Substitution  of  an  alkyl  group  in  the    —OH  group  of 
hydroxy-  or  amino-phenols  destroys  the  developing  properties ; 

(e)  Substitution  of  an  alkyl  group  in  the   —  NH2  group  of  an 
amino-phenol  raises  the  reduction  potential; 

(f)  Any  or  all  of  the  hydrogen  atoms  of  the  amino  groups 
in  an  amine  may  be  substituted  by  alkyl  groups,  thus  increasing 
the  reduction  potential ; 

(g)  If  the    -NH2  group  of  an   amino-phenol   or  diamine 
be  substituted  to  give  a  glycine  the  reduction   potential  is 
lowered ; 

(h)  The  reduction  potential  is  increased  by  substituting  a 
third  active  group  in  the  nucleus.  This  substitution  makes 
the  meta  compounds  developers  if  the  third  group  is  not  in 
the  symmetrical  position. 


The  above  summarizes  those  conclusions  of  Lumiere  and 
Seyewetz  and  of  Andresen,  which  apply  to  substances  within 
the  ordinary  range. 

Valuable  as  these  so-called  "rules"  have  been,  it  is  probable 
that  some  of  them  would  be  discredited  could  the  necessary 
measurements  be  obtained.  While  in  general  they  are 
correct  as  to  the  kind  of  substances  which  possess  the  develop- 
ing function  to  any  degree,  they  are  wrong  in  certain  respects 
as  to  the  relative  energies  possessed  by  the  substances  in 
question,  especially  as  to  the  effect  of  certain  substitutions 
on  the  developing  energy.  We  know  of  no  accurate  quantita- 
tive experimental  work  in  photography  except  the  limited 
results  of  Sheppard,  and  of  Sheppard  and  Mees,  which  could 
possibly  justify  and  support  these  conclusions  as  to  the  effects 
of  structure.  While  admittedly  correct  in  many  cases,  the 
conclusions  must  have  been  reached  mainly  by  a  priori 
chemical  reasoning,  as  they  were  evidently  submitted  to  only 
rough  qualitative  tests,  which  are  by  no  means  conclusive. 

1  Compiled  from  the  above  rules. 

18 


THE  THEORY  OF  DEVELOPMENT 

The  molecular  structure  of  the  reducing  agent  undoubtedly 
has  a  considerable  effect  on  the  developing  properties  in  so  far 
as  it  influences  or  conditions  the  several  specific  properties  of 
the  reducer,  but  a  classification  of  developers  on  the  basis 
of  free  molecular  energy  alone  would  not  agree,  strictly  at 
least,  with  a  classification  made  according  to  developing 
properties.  At  present  there  is  no  method  for  determining 
the  true  chemical  affinity  or  reduction  potential  of  the  devel- 
oping agent  per  se,  and  therefore  the  classification  of  organic 
reducers  given  is  made  according  to  apparent  developing 
properties;  and  what  is  referred  to  as  reduction  potential  is 
relative  energy  from  the  standpoint  of  practical  development. 

To  furnish  evidence  on  the  question  of  structure  especially 
it  was  proposed  to  study  the  reduction  potentials  and  devel- 
oping characteristics  of  a  large  number  of  compounds. 
Although  this  plan  has  not  yet  been  completed,  much  work 
has  been  done  on  many  of  the  substances. 

Table  1  shows  part  of  the  original  plan.  The  compounds 
marked  "X"  in  Table  1  and  those  listed  in  Table  2  have  been 
examined. 

This  investigation  has  been  limited  by  the  very  great 
difficulties  encountered  in  the  course  of  the  work.  In  the 
first  place,  it  was  found  practically  impossible  to  prepare 
some  of  the  compounds  required  in  a  sufficiently  pure  state. 
From  the  experience  of  the  Organic  Chemical  Department  of 
this  laboratory  in  the  preparation  of  substances  of  this  char- 
acter, it  is  doubtful  whether  some  of  the  photographic  devel- 
oping agents  mentioned  by  previous  investigators  have  ever 
been  prepared  in  such  a  form  that  their  real  photographic 
properties  could  be  determined.  Other  difficulties  arose  in 
working  out  suitable  experimental  methods  and  in  securing 
sufficiently  accurate  and  reliable  data.  However,  the  results 
of  the  experimental  work  here  presented  are  given  with  a  very 
reasonable  assurance  that  they  are  the  best  obtainable  under 
the  most  favorable  conditions.  Photographic  research  of 
this  kind  is  an  especially  slow,  tedious,  and  expensive  process, 
a  fact  which  is  not  always  fully  appreciated. 

CHEMICAL  THEORY  OF  THE  METHOD  EMPLOYED  IN  DETERMINING 
REDUCTION    POTENTIAL 

The  principal  method  employed  in  determining  relative 
reduction  potentials  depends  on  the  restraining  action  of 
soluble  bromides  when  used  with  the  reducers  in  question, 
a  method  first  applied  by  Sheppard1.  A  soluble  bromide, 

1  Sheppard,  S.  E.,  Theory  of  alkaline  development.     J.  Chem.  Soc.  39:  530.     1906. 

19 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


Table  I 

SYSTEMATIC    STUDY    OF    DEVELOPING    PROPERTIES 

j 

Two     -OH     croup*  Two     -HE*     groups  One  -OH  +  on*  -KB* 

para  orttxo  para  onh'o  para  ortho 


r^S*,  r^- 

»  matnylatlon  I  ill 

VQ 


Siae-oh&ln-BBtbylatlon 


.CH, 


reaotl^  J*^ 

group  I 

u 


0! 


X 

H(CH,). 

0 


Ctlorinitlon 


Kuolear  and  side- 
chain iBflthylatlo 


Change  to  Glyclno 


The  reduction  potentials  and  developing  characteristics  of 
the  compounds  marked  "X"  have  been  .studied. 


20 


THE  THEORY  OF  DEVELOPMENT 

Table  II 

ADDITIONAL     COMPOUNDS    WHICH    HAVE    BEEN     EXAMINED    FOR 
REDUCTION  POTENTIAL  AND  DEVELOPING  CHARACTERISTICS 

Ferrous  oxalate 

Pyrogallol 
Phonyl  hydrazine 


Dicblor  hydroqulnooe 
101 


Bronx  hydroquinone 


Dlbroa  hydroaulnone 


NBa 

NH2.OH.HC1.     Hydroxylamine  hydrochloride. 


21 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

such  as  potassium  bromide,  may  affect  development  (i.  e.,  may 
exert  restraining  action)  in  two  and  possibly  three  ways. 
(It  is  understood  that  the  development  of  a  silver  bromide 
emulsion  is  under  consideration.) 

1.  Soluble  bromides,  being  reaction  products  of  a  reversible 
reaction,  such  as 

-  + 

ONa  O 

+  ~   -^   f"N  + 

+  2Ag  Br   ^-       +  2Ag   +  2Na  Br 

k^          met. 

ONa  O 

h 

lower  the  driving  force  of  the  reaction  in  the  forward  direction. 
This  view  was  first  presented  by  H.  E.  Armstrong,  and  later 
adopted  by  Hurter  and  Driffield  and  by  Luther.1 

2.  The  bromide  depresses  the  concentration  of  silver  ions 
by  the  action  of  the  common  anion,  Br, — a  theory  first  due 
to  Abegg.2 

3.  The  bromide  may  have  a  specific  action  on  the  silver 
halide  other  than  that  mentioned  in  2.     Concerning  such  a 
possibility  we  have  little  knowledge,  but  various  phenomena 
occurring  at  high  concentrations  of  bromide  indicate  effects 
quite  different  from  those  described  in  1  and  2.    (Chapter  IX.) 

Abegg,  applying  physico-chemical  laws,  considered  develop- 
ment as  consisting  of  two  simultaneous  processes — oxidation 

of    the  developer   ll  — >     R,  and    reduction    of    the  silver 

+ 
ion  Ag  — >  Agmet.  each  tending  to  reach  equilibrium  as  defined 

+ 

by  fixed  values  of  the  ratios  =-=*  and  pr-^ — r 

[R]  [Agmet.] 

For  a  "strong"  developer  the  value  of  the  equilibrium  ratio 

for  the  reaction  Ag — >  Agmet.  is  greater  than  for  a  "weak" 
one — i.  e.,  the  stronger  developer  can  reduce  silver  from  a 
solution  weaker  in  silver  ions  (richer  in  bromine  ions).  The 
bromide  susceptibility  is  therefore  a  measure  of  the  developing 
potential  of  the  reducing  ion. 

Further,  for  the  reaction  above,2  the  potential  of  the  reducing 
ion  R  in  the  process  of  losing  one  electron  at  equilibrium  is 

fRl 
RT  log  -^  and  this  must  be  equal  (but  opposite  in  sign)  to 

[R] 

1  For  citations,  see  bibliography  appended. 
J  Sheppard — for  citation,  see  bibliography. 

22 


THE  THEORY  OF  DEVELOPMENT 

+ 

that  of  Ag  in  acquiring  one  electron  —  RT  log  r-?  --  ' 

l^gmet.J 

[Ag]  [Br] 
Also'      [AgBr] 

And  since  [AgBr]  is  in  excess  and  may  be  considered  constant, 
[Ag]  [Br]    ==  K  and  [Ag]    =      -- 


Hence,  the  potential  of  the  ion  R  in  passing  to  the  higher 
oxidation  stage  R  may  be  written 

-A  ==  RT  (log  [A+g]  -  log  [Agmet.]) 

=  RT  (log  k  -  log  [Br]  -  log  [Agmet.]) 

where  k  is  the  dissociation  constant  of  the  silver  bromide  and 
log  [Agmet.]  is  a  constant  (for  fixed  exposure),  log  [Br]  being 
the  only  variable  in  the  right-hand  member.1  Hence  the 
reduction  potential  varies  with  log  [Br],  or  the  logarithm  of 
the  concentration  of  bromine  ions  corresponding  to  the 

[Ag] 
equilibrium  value  of-7-r 

[Agmet.l 

The  above  is  based  on  the  assumption  that  the  bromide 
acts  chiefly  by  depressing  the  dissociation  of  the  silver  bro- 
mide, which  is  probably  the  case.  However,  taking  all  the 
evidence  into  account,  it  is  not  justifiable  to  assume  that  it  is 
ever  the  only  effect,  or  always  the  chief  one.  The  form  of 
the  function  relating  reduction  potential  to  bromide  concen- 
tration is  therefore  unknown,  and  no  assumptions  will  be 
made  regarding  it.  For  simplicity  the  results  interpreted  as 
relative  reduction  potentials  are  considered  as  measured  by 
the  concentrations  of  bromide  involved. 

It  should  be  especially  noted  also  that  in  the  present 
investigation  the  relations  are  not  expressed  in  terms  of  the 
concentrations  of  the  bromine  ion,  but  in  terms  of  potassium 
bromide  concentrations,  this  being  a  logical  procedure  until 
the  true  relations  are  established.  The  reduction  potentials 
as  measured  by  the  methods  employed  will  be  in  the  proper 
order,  if  not  of  the  right  magnitude,  and  all  the  results  may 
be  converted  when  further  information  warrants. 

In  accordance  with  the  deduction  made  above  Abegg 
suggested  as  a  measure  of  the  potential  the  amount  of  bromide 

1  The  author  is  indebted  for  this  suggestion  to  Dr.  S.  E.  Sheppard. 

23 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

against  which  a  reducing  agent  can  just  develop.  But,  as 
Sheppard  points  out,  this  method  fails  with  most  organic 
developers  because  the  oxidation  products  are  not  stable  and 
their  concentrations  are  indeterminate.  Hence  the  equilibrium 

[R"I 

condition  is  not  maintained  by  -=r-  and  the  energy  is  a 
function  of  the  time. 

Sheppard's  method  was  to  compare  the  concentrations  of 
bromide  required  by  different  developers  to  produce  the 
same  depression  in  density  at  the  same  degree  of  development. 
But  Sheppard  did  not  give  any  clear  quantitative  relation  as 
the  basis  of  his  method,  and  certain  of  the  conclusions  reached 
were  erroneous  through  lack  of  sufficient  data.  By  use  of 
experimental  results  now  available,  however,  the  method, 
with  modifications,  can  be  justified.  Its  bearing,  in  terms  of 
well  established  chemical  theories  of  reduction  potential,  is 
still  somewhat  obscure.  It  is  believed  that  when  certain 
electrochemical  data  are  secured  the  relationship  will  be 
established.  At  any  rate,  the  photographic  action  of  bromide 
has  been  thoroughly  investigated  and  some  definite  concep- 
tions have  resulted. 

It  may  be  assumed  from  data  given  below  that: 

1 .  The  presence  of  bromide  causes  an  increase  in  the  reaction 
resistance ; 

2.  The  more  powerful  the  developer,  the  greater  the  concen- 
tration   of    bromide    against   which    it    can    force    the    ratio 

,  ,  past  the  value  at  which  metallic  silver  is  precipitated. 

[Agmet.] 

That  is  (as  stated  above),  a  powerful  developer  can  develop 
in  the  presence  of  a  higher  concentration  of  its  reaction 
products  than  a  weak  one,  or  it  can  reduce  silver  from  a 
solution  weaker  in  silver  ions.  Also,  the  more  powerful  the 
developer,  the  greater  the  concentration  of  bromide  required 
to  produce  a  given  change  in  the  amount  of  work  done; 

3.  The  bromide  susceptibility  is  a  measure  of  the  potential 
of  the  reducing  ion,  though  the  quantitative  relations  are  not 
definitely  known  at  present; 

4.  The  bromide  susceptibility    may  be    measured  by    the 
concentration  of  bromide  required  to  produce  a  given  change 
in  the  amount  of  work  done; 

5.  The  change  in  the  total  amount  of  work  which  can  be 
done  may  be  found  photographically  by  determining  the  shift 
of  the  equilibrium — i.  e.,   the  lowering  of  the  maximum  or 
equilibrium  value  of  the  density  for  a  fixed  exposure.     The 

24 


THE  THEORY  OF  DEVELOPMENT 

reduction  potentials  will  then  be  related  as  the  concentrations 
of  bromide  required  to  produce  the  same  amount  of  change, 
or  more  probably  as  the  logarithms  of  these  concentrations. 

The  last  is  essentially  the  principle  of  Sheppard's  method, 
although  it  could  not  be  shown  at  the  time  that  the  quantity 
measured  was  the  shift  of  the  equilibrium. 

It  will  be  shown  that  several  methods  place  developers  in 
the  same  order,  and  much  indirect  evidence  indicates  that  the 
fundamental  conceptions  of  the  theory  are  correct  or  nearly  so. 

DETAILS    OF    THE    EXPERIMENTAL    WORK 

It  now  becomes  necessary  to  consider  some  of  the  basic 
principles  of  those  quantitative  photographic  methods  which 
are  often  incorrectly  grouped  under  the  term  sensitometry. 
Various  details  of  the  experimental  wrork  are  presented  first, 
as  leading  up  to  the  interpretation  of  the  data. 

The  methods  adopted  are  similar  to  those  of  Hurter  and 
Drimeld  and  of  Sheppard  and  Mees.  For  the  convenience 
of  readers  not  familiar  with  the  work  of  these  investigators, 
it  is  reviewed  below  in  so  far  as  is  necessary  to  an  understand- 
ing of  the  principles  involved. 

To  obtain  quantitative  measurements  of  the  character  of  a 
photographic  plate,  or  to  determine  the  effect  of  any  factor  on 
the  development  process,  it  is  necessary  to  carry  out  the 
following  steps : 

(a)  Exposure  of  the  plate  in  a  definite  manner,  for  a  definite 
time; 

(b)  Development  under  known  conditions; 

(c)  Measurement  of  the  resulting  deposit  of  silver; 

(d)  Interpretation  of  the  data  obtained. 

The  extent  to  which  this  plan  is  followed  depends  of  course 
on  the  information  desired.  For  the  present  purpose  certain 
phases  of  the  work  are  necessarily  quite  extensive.  For 
example,  while  the  effect  of  a  wide  range  of  exposures  is  not 
studied,  the  development  of  the  plates  is  carried  out  for  a  long 
time  under  varied  conditions,  and  the  data  are  carefully 
studied.  The  physical  side  of  the  photographic  process  may 
be  ignored  so  long  as  the  necessary  conditions  are  constant 
throughout.  Thus  photographic  methods  are  turned  to 
the  uses  of  chemistry,  and  the  present  investigation  is  there- 
fore as  much  a  chemical  as  a  photographic  one. 

(a)   Exposure  of  the  Sensitive  Material. 

The  plates  were  exposed  in  a  sensitometer,  or  exposing 
machine,  which  by  means  of  an  electrically  controlled  sliding 
metal  plate  placed  immediately  itu  front  of  the  sensitive 

25 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

material  exposes  the  latter  in  a  series  of  steps  for  known 
times  to  a  standard  light  source.  This  type  of  sensitometer 
has  been  described  by  Jones.1  The  light  source  used  was  the 
acetylene  burner  described  by  Mees  and  Sheppard,2  screened 
to  average  daylight  quality  with  a  Wratten  No.  79  filter. 
The  times  of  exposure  represent  a  logarithmic  exposure  scale, 
or  a  series  of  times  increasing  by  consecutive  powers  of  some 
number,  usually  2,  \/2~,  or  1.58  (of  which  logic  =  0.2).  This 
scale  is  used  because  it  is  found  that  the  blackening  produced 
upon  development  increases  with  the  increase  of  exposure 

(exposure  =  product  of  light 
flux  multiplied  by  the  time) 
in  such  a  way  that  the  darken- 
ing, expressed  in  terms  of  density 
plotted  against  the  logarithm  of 
the  exposure,  gives  a  curve  which 
shows  the  character  of  the  emul- 
sion. Such  a  curve  is  generally 
-  referred  to  as  an  H.  and  D. 


Fj     j  curve.     (See  Fig.  1.)     The  den- 

sity is  defined  as  follows: 
T   =  transmission  of  the  deposit  on  the  developed  plafe; 

—  =  opacity  of  the  deposit   =  0; 

log™  0  =  density   =  D. 

Using  a  logarithmic  scale  of  exposures  as  abscissae  and  D  as 
ordinates,  it  is  evident  that  the  successive  pairs  of  exposure 
steps  will  be  separated  by  equal  distances  on  the  horizontal 
axis. 

D  is  proportional  to  the  amount  of  metallic  silver  present  in 
a  given  area  of  the  deposit  under  average  conditions.  The 
H.  and  D.  curve  therefore  shows  the  relation  between  the 
amount  of  silver  deposited  and  the  exposure  for  a  fixed  degree 
of  development. 

(b)  Method  of  Development. 

To  insure  standard  conditions  during  the  development  of 
the  plates  it  is  necessary  to  provide  for  efficient  stirring  of  the 
developer,  to  maintain  a  constant  temperature,  and  to  see  that 
the  times  of  development  are  accurate.  The  question  of 
stirring  during  development  is  a  rather  troublesome  one,  as 
some  developers  require  much  more  vigorous  stirring  than 
others  to  ensure  uniform  development.  This  of  course  means 

1  For  citation  see  bibliography. 

2  Mees,  C.  E.  K.,  and  Sheppard,  S.  E.,  New  investigations  of  light  sources.      Phot.  J. 
53:  287.      1910. 

26 


THE  THEORY  OF  DEVELOPMENT 

that  it  is  more  necessary  to  keep  the  oxidation  products 
thoroughly  washed  out  of  the  emulsion  in  some  cases  than  in 
others. 

There  are  two  disadvantages  in  the  use  of  a  tray  for  devel- 
oping. First,  the  mechanical  rocking  of  a  tray  (motion  in  a 
vertical  plane)  is  very  likely  to  produce  streaks,  though  when 
this  is  done  by  hand  the  motion  is  more  irregular  and  the 
results  are  better.  Secondly,  a  large  surface  of  the  developer 
is  exposed  to  the  air.  The  use  of  a  water- jacketed  tube  as 
shown  in  Fig.  2  does  away  with  these  objectionable  features. 


Oil 


Fig.  2 

This  apparatus  consists  of  a  heavy  glass  tube  T,  seven  inches 
long  and  one  and  one-quarter  inches  in  diameter,  within  a 
stoppered  glass  jar.  The  space  surrounding  the  inner  tube 
is  filled  with  water  at  20°  C.  from  a  centrifugal  pump  in  a 
thermostat.  Concentric  rubber  tubes,  A  and  B,  with  a  metal 
connector  C,  connect  with  the  pump  so  that  the  water  from 
the  pump  is  thermally  shielded  by  the  water  returning  to  the 
thermostat.  A'  and  B'  are  flexible  rubber  tubes  connecting 
with  the  water-jacket.  The  plates  used  were  one  inch  wide 
by  four  and  one-quarter  inches  long  and  were  developed  two 
at  a  time  in  the  silver-plated  holder  H,  shown  at  the  side. 
The  prongs  at  the  bottom  of  the  holder  were  fitted  with  soft 
rubber  to  prevent  breakage  of  the  inner  tube.  About  60  cc. 
of  developer  were  poured  into  the  tube  T,  the  plate  holder 
and  stopper  inserted,  and  the  whole  wras  shaken  by  hand> 

27 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

This  quantity  of  developer  left  an  air  space  large  enough  to 
assure  thorough  shaking,  which  was  aided  by  the  movement 
of  the  plate  holder. 

Sufficient  skill  was  acquired  in  the  use  of  this  device  to 
make  possible  a  time  of  development  of  fifteen  seconds  with 
an  accuracy  of  ten  per  cent.  For  longer  times  greater  accuracy 
was  obtained.  Various  timing  devices  were  used.  Fresh 
developer  was  used  for  each  pair  of  plates.  In  some  cases  it 
was  necessary  to  economize  on  developer  because  of  the  small 
quantity  of  developing  agent  obtainable  compared  with  the 
large  amount  of  experimental  work  for  which  it  was  to  be 
used.  The  water- jacketed  tube  described  was  especially 
advantageous  in  this  respect. 

A  silver-plated  metal  water- jacketed  tray  provided  with  a 
cover  was  used  for  some  of  the  work,  and  for  very  long  times 
of  development  a  silver-plated  cylindrical  water-jacketed 
tank,  fitted  with  a  revolving  shaft  with  fan  stirrer  at  the 
bottom  and  holders  for  the  two  plates  mounted  above  the 
stirrer  was  useful.  The  shaft  was  revolved  slowly  by  means 
of  an  electric  motor. 

The  three  developing  apparatus  were  compared  on  numerous 
occasions.  No  definite  conclusions  were  reached  as  to  which 
gave  most  uniform  results,  but  for  constant  use  it  was  found 
that  glass  vessels  like  the  developing  tube  first  described  are 
rather  more  satisfactory  than  the  metal  containers  as  the  silver 
plating  wears  off  and  the  exposed  metal  is  apt  to  cause  trouble. 

Developers  Used.  In  all  comparisons  of  developing  agents 
the  same  concentrations  oJj  the  necessary  ingredients  were 
used.  The  formula  adopted  is: 

Developing  agent M/20; 

Sodium  sulphite 50  gms. ; 

Sodium  carbonate 50  gms.; 

Water  to 1000  cc. 

In  some  cases  the  sodium  carbonate  was  omitted,  and  in  some 
cases  caustic  soda  was  used.  These  exceptions  are  noted  in 
the  tables.  The  concentration  M/20  was  used  except  in 
those  cases  where  the  developing  agent  was  not  soluble  in  this 
proportion.  Exceptions  are  noted  in  the  tables.  On  the 
whole,  the  concentrations  in  the  above  formula  give  satis- 
factory developers,  though  not  necessarily  as  good  as  could 
be  made  in  individual  cases  by  careful  adjustment  of  the 
concentrations  of  the  various  constituents. 

28 


THE  THEORY  OF  DEVELOPMENT 

As  previously  shown  by  Sheppard  and  Mees,1  Luther  and 
Leubner,2  and  Frary  and  Nietz,3  a  developer  like  that  indicated 
by  the  above  formula  represents  a  very  complex  chemical 
system.  Apparently  the  developing  agent  and  the  sodium 
carbonate  react  to  form  phenolates  to  an  extent  depending  on 
equilibrium  conditions,  and  probably  there  is  a  reaction 
between  the  sulphite  and  the  developing  agent  or  its  pheno- 
lates. The  various  reaction  products  then  hydrolyze  and 
dissociate,  so  that  the  developing  properties  depend  on  a  very 
complicated  adjustment.  It  is  obvious  that  in  the  absence 
of  definite  knowledge  of  these  reactions  a  comparison  of  two 
developing  agents  under  identical  chemical  conditions  is 
impossible.  Even  with  standard  concentrations  of  alkali 
and  sulphite  there  is  no  assurance  that  hydroquinone  used 
in  the  above  formula  is  under  chemical  conditions  identical 
with  those  under  which  paraminophenol  would  be.  The 
hydroquinone  probably  forms  a  mixture  of  the  two  phenolates 
which  reacts  to  a  certain  extent  with  the  sulphite.  These 
reactions  would  be  different  or  proceed  to  a  different  equili- 
brium point  with  paraminophenol,  and  the  state  of  the  two 
systems  would  be  different  also  because  of  variations  in  the 
degrees  of  hydrolysis  and  dissociation. 

The  best  that  can  be  done  at  present,  therefore,  is  to  use 
a  standard  method  of  comparison  by  employing  always  the 
same  concentrations.  This  will  give  the  right  order  as  to 
the  reducing  energy  of  most  developers,  though  not  properly 
distinguishing  between  those  nearly  alike.  It  should  be 
pointed  out  that  for  these  reasons  (as  well  as  for  others  pre- 
viously mentioned),  the  photographic  method  cannot  be  used 
for  determining  the  true  relative  affinities  of  the  reducing 
agents  themselves,  but  it  is  valuable  in  giving  a  classification 
of  these  substances  as  developers  when  used  in  the  ordinary 
way.  From  the  standpoint  of  photographic  theory  the  latter 
is  more  important. 

Emulsions  used.  Seed  23  and  Seed  30  emulsions  were  used 
for  most  of  the  experiments,  though  a  number  of  special 
emulsions  (noted  below)  were  prepared.  Eastman  Portrait 
film  was  also  used.  Though  much  of  the  work  was  done 
with  plates,  film  is  more  satisfactory  in  many  ways. 

1  Sheppard,  S.E.,  and  Mees,  C.  E.K.,  Investigations  on  the  theory  of  the  photographic 
process. 

2  Luther,  R.,  and  Leubner,  A.,  The  chemistry  of  hydroquinone  development.    Brit.  J. 
Phot.  59:  632,  653,  673,  692,  710,  729,  749.     1912. 

3  Frary,  F.  C.,  and  Nietz,  A.H.,  The  reaction  between  alkalies  and  metol  and  hydro- 
quinone in  photographic  developers.     J.  Amer.  Chem.  Soc.  37:  2273.     1915. 

29 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

(c)  Measuring  the  Silver  Deposits. 

The  density  (silver  deposit)  was  determined  by  measuring 
the  amount  of  light  transmitted,  using  the  Martens  pho- 
tometer. Special  precautions  were  taken  to  minimize  the 
effects  of  stray  light  in  and  around  the  instrument.  Measure- 
ments were  made  with  the  emulsion  side  of  the  negative  in 
contact  with  a  diffusing  surface,  a  piece  of  ground  pot  opal 
glass  being  used.  For  the  high  densities  a  powerful  light, 
housed  in,  with  a  pair  of  condensers,  was  used,  and  a  compen- 
sating photographic  density  was  placed  in  the  comparison 
field  to  increase  the  accuracy  of  reading.  The  densities  as 
read  and  used  represent  the  total  deposit,  no  subtraction  of 
the  fog  reading  being  made.  Reasons  for  this  will  be  given 
in  the  chapter  on  the  distribution  of  fog. 

(d)  Interpretation  of  the  Data. 

In  order  to  understand  fully  the  results  obtained  in  the 
experiments,  it  is  necessary  to  interpret  them  according  to 
certain  fundamental  principles  which  are  reviewed  in  the  next 
section. 

SENSITOMETRIC    THEORY 
I.     PRINCIPLES    ESTABLISHED    BY    OTHER   INVESTIGATORS. 

The  results  obtained  by  Sheppard  and  Mees  confirmed  and 
amplified  those  of  Hurter  and  Drifrield  in  the  field  of  quantita- 
tive photographic  research.  The  significance  of  the  H.  and 
D.  curve,  the  general  character  of  which  was  shown  in  Fig.  1, 
has  been  mentioned.  Although  in  the  figure  the  curve  is 
drawn  as  having  a  considerable  straight  line  portion  any 
equation  representing  it  must  indicate  that  it  has  a  point  of 
inflection  and  with  certain  emulsions  precise  measurements 
show  this  to  be  the  case.  However,  under  most  conditions 
(within  the  errors  of  observation),  a  considerable  portion  of 
the  curve  is  a  straight  line.  In  the  present  work  emulsions 
giving  a  rather  long  straight  line  region  were  used,  and  in 
the  later  discussion  the  "toe"  and  "shoulder"  of  the  curve 
are  not  considered. 

The  straight  line  portion  of  the  curve  has  the  equation 

D   =  y  (log  E   -  log  i) 

where  y  is  the  slope,  and  log  i  is  the  intercept  on  the  log  E 
axis.  y  is  termed  the  development  factor,  log  i  the  inertia 
point,  and  i  the  inertia  (expressed  in  the  proper  exposure 
units). 

If  a  number  of  plates  which  have  been  given  the  same  ex- 
posure in  the  sensitometer  are  developed  under  constant 

30 


THE  THEORY  OF  DEVELOPMENT 


conditions  for  varying  times,  the  densities  plotted  against  log 

E  as  before  give  a  series  of  curves  for  the  different  times  of 

development  of  the  kind  shown  in  Fig.  3. 

The  density  increases  with 
development  until  a  limit  is 
reached,  and  on  infinite  develop- 
ment (for  a  non-fogging  de- 
veloper and  emulsion)  the  up- 
permost curve  is  obtained.  The 
laws  relating  to  the  growth  of 
density  with  time  are  discussed 
in  a  later  chapter.  For  the 
present  it  is  sufficient  to  note 
that  the  development  factor,  y, 
increases  with  time  of  develop- 

ment   to    a    limiting    value,    but    that,    for    the   case  shown, 

the  inertia  point  (log  i)  does  not  change   with    time.     Also, 

y  is  independent  of  the  exposure. 

The  so-called  "law  of  constant  density  ratios"  of  Hurter  and 

Driffield   is   a   necessary   consequence   of   the   above   results. 

This    is    illustrated    for    the    two    exposures    represented    by 

log  E  =  0.9  and  log  E  =1.2. 


Fig.  3 


D, 


DV 


That  is,   for  the  straight  line  region,   the  density  increases 
proportionately  with  time  of  development. 

More  meaning  may  be  attached  to  the  constant   y.      Over 


the  straight  line   region   the  slope    tan   a 


The  rate  of  growth  of  density  with  exposure  is  interpreted 
photographically  as  the  "contrast",  y  may  therefore  be 
termed  the  contrast  of  the  negative. 

Although  in  the  above  case  (Fig.  3)  the  inertia  is  constant 
with  increasing  time  of  develop- 
ment, this  is  not  true  when 
soluble  bromides  are  present 
in  the  developer.  Moreover, 
at  the  same  degre  of  develop- 
ment (same  development  factor, 
y)  the  plate  curve  is  "shifted" 
from  its  normal  position.  These 
results  are  illustrated  in  Fig.  4. 
The  straight  line  portions  only 
are  considered. 

31 


Fig.  4 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Curves  for  the  unbromided  and  bromided  developers  at 
three  degrees  of  development  are  shown.  This  result  was 
referred  to  by  Hurter  and  Driffield  and  by  Sheppard  and 
Mees  as  a  lateral  shift  of  the  plate  curve,  though  the  latter 
spoke  of  the  "density  depression"  (A-D  in  the  figure),  as  the 
lowering  of  density  produced  by  the  bromide  in  plates  at  the 
same  y.  They  stated  that  the  effect  of  inertia  change  or 
density  depression  wears  off  with  time,  so  that  finally  the  same 
inertia  (same  D)  is  reached  as  if  no  bromide  were  present. 
This  conclusion  has  not  been  confirmed  in  the  present  work, 
the  result  being  in  some  cases,  however,  obscured  by  the 
growth  of  fog. 

Further,  the  amount  of  the  shift  of  the  curve  (or  the 
depression)  produced  by  a  given  amount  of  bromide  varies 
with  the  developer,  it  being  greater  for  hydroquinone  than 
for  paraminophenol,  for  instance.  Also,  bromide  is  found 
to  have  a  marked  effect  on  the  time  required  before  develop- 
ment begins — the  "time  of  appearance."  This  also  varies 
noticeably  with  the  developer.  It  is  more  or  less  evident, 
therefore,  that  developers  differ  in  their  "susceptibility"  to 
bromide,  and  that  their  bromide  sensitiveness  is  connected 
with  their  developing  energies,  as  discussed  above. 

Sheppard's  method  of  determining  the  relative  reduction 
potentials  of  developers  by  means  of  the  density  depression 
with  bromide  may  now  be  briefly  outlined,  though  the  calcu- 
lation employed  will  not  be  clear  until  the  velocity  of  develop- 
ment and  the  velocity  constant  have  been  considered.  How- 
ever, neglecting  these  for  the  time  being,  the  method  in  general 
was  to  determine  the  depression  for  a  definite  degree  of 
development  with  the  developers  to  be  studied,  the  depression- 
bromide  concentration  relation  having  been  established  for 
ferrous  oxalate.  The  concentration  of  bromide  necessary 
to  produce  the  same  depression  at  the  same  degree  of 
development  was  then  calculated  for  each  developer.  By 
comparing  the  concentrations  of  bromide  thus  found  necessary 
to  produce  the  same  depression,  the  following  values  were 
obtained : 

Relative 
Reduction  Potential 

Ferrous  oxalate 1.0 

Hydroxylamine :  .  .  1 . 13 

Hydroquinone 0.5-0.7 

Paraminophenol ..3.4 

Sheppard  worked  only  over  the  range  of  bromide  concentra- 
tions where  practically  the  same    y    is  obtained  in  a  given 

32 


THE  THEORY  OF  DEVELOPMENT 

time  as  if  no  bromide  were  used.  The  depressions  under 
these  conditions  are  small  and  the  errors  are  proportionately 
large.  Furthermore,  this  method  cannot  be  used  for  all 
developers,  as  concentrations  of  bromide  sufficient  to  cause 
much  depression,  require  a  much  longer  time  to  reach  the 
same  development  factor  with  some  developers  than  with 
others. 

Though  the  fundamental  basis  for  the  method,  as  stated 
above,  was  not  well  established,  the  measurements  undoubt- 
edly show  the  relative  shifts  of  the  equilibrium  points,  and 
accordingly  place  the  developers  in  the  right  order. 

II.     NEW       CONCEPTIONS       INTRODUCED       IN       THE        PRESENT 
INVESTIGATION. 

In  the  present  work  the  effect  of  bromide  on  development 
was  investigated  and  as  a  result  some  modifications  in  the 
above  theory  have  been  made.  A  new  method  of  interpreting 
the  depression  data  has  been  adopted.  This  revised  theory 
is  based  on  a  study  of  about  25,000  sensitometric  strips, 
representing  all  types  of  emulsions  and  a  much  wider  range 
in  developers,  bromide  concentrations,  etc.,  than  previously 
used.  The  general  conclusions  reached,  relative  to  the 
bromide  depression  method,  are  explained  below.  The 
experimental  results  supporting  the  method,  and  obtained 
by  means  of  it,  constitute  the  second  and  third  chapters  of 
this  monograph,  and  the  effects  of  bromide  on  the  velocity 
are  considered  in  later  chapters. 

It  was  found  that  with  all  normal  plates  and  normal 
unbromided  developers  the  straight  line  portions  of  the  H. 
and  D.  curves  for  varying  times  meet  in  a  point  on  the  log  E 
axis  for  the  entire  range  of  times  where  fog  is  not  produced 
to  any  great  extent.  (Excessive  fog  is  usually  considered  as 
being  greater  in  density  than  0.5  or  more.)  This  is  the 
condition  represented  by  Fig.  3.  Consequently  log  i  or  the 
inertia  point  is  independent  of  the  time  of  development. 
Hurter  and  Driffield  and  also  Sheppard  and  Mees  found  this 
to  be  true  and  stated  it  as  a  rule,  though  with  scarcely  sufficient 
proof. 

It  will  be  easier  to  ascertain  whether  or  not  the  curves 
meet  in  a  point  by  applying  the  theory  about  to  be  described 
than  by  actually  extending  the  lines  of  all  the  curves.  More- 
over, the  personal  error  is  greatly  lessened,  because  at  low 
gammas  the  intersection  point,  or  log  i  value,  can  be  varied 

33 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

greatly  for  only  a  small  change  in  gamma.  Also  the  new 
method  is  of  more  value  in  studying  the  whole  subject  of 
development. 

The  equation  for  the  straight  line  portion  of  the  curve,  as 
previously  stated  is 

D   =  y  (log  E   -  log  i)  (1) 

If  for  a  fixed  value  of  log  E  (log  E  =  constant)  we  plot  D 
against  y  for  each  separate  time  of  development  (different 
values  of  y)  we  shall  obtain  a  straight  line  through  the  origin 
(D  =  O,  y  =  O)  if  log  i  is  a  constant,  because  the  equation 
for  each  curve  is 

D   =  y  0, 
where  0   =  log  E   —  log  i   =  constant.  (2) 

That  is,  the  rate  of  variation  of  density  with  gamma,  — —   is  0 

and  the  density-gamma  function  is  one  of  constant  slope  — 
i.  e.,  a  straight  line. 

The  results  of  several  hundred  examinations  were  plotted 
(D  against  y  for  a  given  exposure)  and  in  many  cases  the 
data  were  least-squared  to  make  sure  of  the  lines  passing 
through  the  origin.  In  this  way  the  method  was  well  estab- 
lished for  the  normal  case. 

Next,  data  for  bromided  development  were  examined  and 
plotted  in  the  same  manner  to  determine  the  character  of 
the  Z)-y  curves.  These  were  straight  lines  also,  but  gener- 
ally they  did  not  pass  through  the  origin,  having  a  positive 
intercept  on  the  y  axis.  This  fact  led  to  the  formulation  of 
more  general  conceptions. 

Let  us  assume  any  system  of  straight  lines  (representing  the 
H.  and  D.  curves)  of  varying  slope,  intersecting  in  any  point 
on  the  log  E  axis  or  below  it,  which  correspond  to  plates 
developed  for  different  times  and  therefore  to  different 
gammas.  The  coordinates  of  the  point  of  intersection  are 
a  and  &,  where  a  is  the  abscissa  expressed  in  units  of  log  E, 
and  b  the  ordinate  expressed  in  units  of  density.  It  is  con- 
venient to  use  a  log  E  scale  of  relative  values  so  that  a  is 
always  positive,  b  is  always  negative  or  zero.  From  the 
system  of  curves  the  following  equation  can  be  written  to 
express  density  at  fixed  exposure  in  terms  of  the  coordinates 
of  the  point  of  intersection : 

D-b 


log  E  —  a 
or         D   =  y  (log  E  -  a)   +  b.     (See  Fig.  5.)  (3) 

34 


THE  THEORY  OF  DEVELOPMENT 

It  is  obvious  from  this  general 
equation  (and  from  geometric 
considerations)  that  so  long  as 
the  straight  lines  meet  in  a 
point  the  relation  between 
density  and  gamma  is  expres- 
sed by  the  equation  of  a  straight 
line,  which  can  be  written  in 
another  form — 

D  =  0  (y  -  A)  =  6  y  -  A  0,    (4) 

where  6  is  the  slope  of  the  line 

(D,  y)  and  A  the  intercept  on  the  gamma  axis.  By  com- 
paring equations  3  and  4 

6   =  log  E   —  a,  and  (5) 

b   =    -Ad.  (6) 

Equation  4  describes  a  density-gamma  straight  line  of  slope  0 
and  intercept  A  on  the  y  axis.  This  is  exactly  what  was 
observed  in  cases  of  bromided  development.  It  is  clear  from 
mathematical  considerations  that  when  this  condition  obtains, 
the  straight  lines  of  the  H.  and  D.  curves  must  meet  in  a 
point.  The  coordinates  of  this  point  are  derived  from  experi- 
mental data  by  the  relations  above.  D  is  plotted  against  y, 
giving  a  straight  line  of  slope  0  and  intercept  A. 

Log  E,  the  standard  or  fixed  exposure  chosen,  is  known. 
Hence  a,  from  equation  5,  is  known,  since 

a   =  log  E  -  0.  (7) 

b  is  determined  by  equation  6. 

Other  relations  may  be  determined  from  those  now  available. 
For  example,  the  gamma-log  i  relation  was  studied  prior  to 
the  adoption  of  the  present  method  and  found  to  be  in  most 
cases  a  hyperbola,  but  errors  in  the  measurement  of  gamma 
at  high  and  low  values  obscured  the  result.  The  present 
interpretation  clears  up  the  matter.  It  can  be  shown  graphic- 
ally that 

r  (8) 


log  i  —  a 

This  is  a  rectangular  hyperbola  referred  to  the  axes  y  =  0 
and  log  i  =  a,  a  fact  which  is  significant  in  connection  with 
bromided  development,  where  log  i  exhibits  considerable 
variation. 


35 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

To  illustrate  further:  from  equation  4,  D  =  6  y  —  A  0. 
Then  if  A  =  0,  D  =  d  y,  or  D  =  y  (log  E  a) 

and  -A  6  =  b  =  0.  Hence  if  the  D-y  straight  line  passes 
through  the  origin  (A  =  0),  b  =  0,  and  the  lines  meet  in  a 
point  on  the  log  E  axis.  Then  a  =  log  i  and  D  = 
y  (log  E  -  log  i),  (the  original  H.  and  D.  equation),  and  again 
we  have  a  description  of  the  family  of  curves  in  Fig.  3. 

The  usefulness  of  the  density-gamma  curve  as  a  criterion 
for  this  characteristic  of  the  H.  and  D.  curves  cannot  be 
questioned.  By  this  means  it  has  been  established  that  not 
only  do  the  curves  for  unbromided  developers  meet  in  a  point 
and  on  the  log  E  axis,  but  also  that  the  curves  for  the  bromided 
developer  meet  in  a  point  of  coordinates  a  and  b. 

Now  let  us  consider  the  effect  of  bromide  on  the  location  of 
the  intersection  point.  The  experimental  data  examined 
show  that  over  the  range  of  bromide  concentrations  employed, 
the  D-y  lines  meet  in  a  point  which  moves  downward  with 
increasing  bromide  concentration.  It  is  thus  seen  that 
Sheppard's  "density  depression"  may  be  interpreted  as  a 
downward  shift  of  the  intersection  point.  There  is  no  logical 
reason  for  assuming  that  the  H.  and  D.  curve  is  shifted 
laterally. 

A  constancy  of  a  and  increase  (negatively)  of  b  indicate 
that  the  intersection  points  move  directly  downward  with 
increase  of  bromide  concentration.  This  can  be  seen  by 
comparing  the  D-y  curves  for  the  different  concentrations 
of  bromide.  From  equation  7,  a  is  constant  if  the  slope  6  is 
constant,  and,  from  equation  6,  the  growth  of  b  (negatively) 
is  shown  by  the  growth  of  A,  the  intercept.  This  is  corrob- 
orated by  the  experimental  work,  as  will  be  shown. 

Therefore  we  may  proceed  to  formulate  the  relations  for 
the  density  depression,  d,  as  measured  by  the  downward 
shift  of  the  intersection  points.  This  will  be  generalized  in 
order  to  include  possible  variations.  The  various  steps  are 
shown  to  make  the  deduction  clear.  From  Fig.  6, 

d    =  WN    =  WT   +  TN; 


==  y;WT   =  (TM)y       =  (at   - 


TN   =    -b,    +  bi. 

Hence,  d  =    -bz  +  bi  4-  (a*  —  0i)  y. 

If  7  be  the  standard  (for  zero  concentration  of  potassium 
bromide)  and  the  a  and  b  values  for  zero  concentration  are 
called  a0  and  b0  ,  the  density  depression,  d,  is  given  by 

d   =    -  b   +b0    +  (a-  a0).  (9) 

36 


THE  THEORY  OF  DEVELOPMENT 


But  for  the   normal   case   b, 


=  0  and  a    =   a0. 


Hence  the 


depression  caused  by  the  concentration  of  potassium  bromide, 
C,  is 

d   =    -b,  (10) 

and  this  is  independent  of  y . 


Fig.  6 

This  relation  is  supported  by  ample  proof  that  for  the 
average  case  a  is  independent  of  the  bromide  concentration 
(i.  e.,  a  =  a?)  and  that  b0  =  0.  There  are,  of  course,  experi- 
mental deviations  from  this,  but  they  represent  relatively 
small  accidental  errors.  Equation  10  is  contradictory  to 
numerous  statements  made  by  other  investigators  that  "the 
effect  of  bromide  wears  off  with  time,"  and  that  the  same 
inertia  is  obtained  on  prolonged  development  with  bromide 
as  without  it.  It  will  be  shown  that  such  statements  are 
erroneous  in  so  far  as  complete  regression  is  concerned,  and 
that  although  such  results  may  be  obtained  at  times,  they  are 
due  mainly  to  the  fog  produced  on  prolonged  development. 
These  cases  may  be  analyzed  by  the  methods  described  here. 

Having  established  a  means  of  obtaining  the  density 
depressions  produced  in  different  developers  by  varying 
concentrations  of  bromide,  it  will  be  possible  to  inquire 
further  into  their  meaning  and  to  study  the  relation  between 
the  density  depression  and  the  concentration  of  bromide 
producing  it. 

37 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Summarizing  briefly,  it  is  found 
that  if  the  density  depression, 
d,  for  any  developer  is  plotted 
against  the  logarithms  of  the 
corresponding  bromide  concen- 
trations, a  straight  line  is  ob- 
tained, like  those  shown  in 

Fig.  7. 

-«v-  w«.c  Tne  equation  for  this  curve  is 

Fig'7  d=  w(logC-logC0),      (11) 

where  m  is  the  slope,  and  log  C0  is  the  intercept  on  the  log  C 
axis.  C0  corresponds  to  the  concentration  of  bromide  which 
is  just  sufficient  to  cause  a  depression  of  density. 

It  is  shown  also  that  the  d-\og  C  lines  for  different  developers 
have  different  intercepts  (different  values  for  log  C0)  but 
have  practically  the  same  slope,  m.  Thus  two  developers 
yield  parallel  lines,  as  shown  in  Fig.  7.  Whether  or  not  m  is 
constant  for  all  plates  and  all  developers  used  could  not  be 
conclusively  proved,  but  it  was  evident  that  in  practically 
all  cases  tested  it  has  very  nearly  the  same  value. 

These  facts  are  of  importance  in  connection  with  the 
reduction-potential  method.  As  stated  above,  C0  is  the 
concentration  of  bromide  required  to  cause  a  perceptible 
shift  of  the  intersection  point.  The  comparison  of  the  values 
of  C0  for  two  developers,  therefore,  gives  a  comparison  of  the 
reduction  potentials  if  we  assume  that  the  change  in  the  loca- 
tion of  the  intersection  point  measures  the  change  in  the 
amount  of  work  done.  Also,  if  m  is  constant,  the  rate  of 
change  of  density  depression  with  bromide  concentration, 

— : — : -^— ,  is  constant  and  independent  of  the  emulsion,  of 

a   log   C 

the  developer,  and  of  the  bromide  concentration.  The 
constant  m  may  therefore  be  connected  with  fundamental 
laws  relating  to  the  development  process. 

These  matters  will  be  taken  up  again  in  connection  with 
the  experimental  evidence,  and  in  addition  other  relations 
of  the  bromide  effect  will  be  developed.  The  plan  of  outlining 
the  propositions  to  be  proved,  or  of  stating  many  of  the 
conclusions  first,  has  been  adopted  because  a  large  mass  of 
photographic  data  presented  without  very  clear  aims  would  be 
quite  confusing,  and  it  is  felt  that  in  an  investigation  of  this 
scope  it  would  be  equally  unsatisfactory  to  develop  all  the 
steps  of  the  theory  along  with  the  experimental  evidence. 

38 


CHAPTER  II 


Developing  Agents  in  Relation  to  their  Relative 

Reduction  Potentials  and  Photographic 

Properties  (Continued] 

EXPERIMENTAL    DATA 

The  following  terminology  has  been  adopted  in  presenting 
the  experimental  data: 

D         Density  (proportional  to  mass  of  silver  in  given  area); 

O         Opacity; 

T        Transmission; 

E        Exposure; 

F        Fog  (density  of  fog  under  any  conditions) ; 

/  Time  of  development; 

ta         Observed  time  of  appearance  of  a  visible  image  during  develop- 
ment (for  standard  exposure) ; 

a         Log  E  coordinate  of  the  point  of  intersection  of  straight  line  por- 
tions of  the  H.  and  D.  curves; 

b          Density  coordinate  for  the  same; 

a0        Value  of  a  when  no  bromide  is  used  (concentration  of  potassium 
bromide  =  0); 

&0        Value  of  b  when  no  bromide  is  used; 

C         Concentration  of  bromide; 

C0       Concentration  of  bromide  which  causes  the  first  perceptible  de- 
pression of  density  (log  C  intercept  of  d-log  C  straight  line) ; 

a        Angle  of  inclination  of  H.  and  D.  straight  line  with  log  E  axis; 
Tan  a  development  factor  or  contrast; 

Q         Slope  of  density-gamma  straight  line; 

A         Intercept  of  density — gamma  straight  line  on  Y  axis; 

d         Density  depression    =   D\  —   Dz  (standard  log  E)  at  same  y  for 
general  case, 

DI  —  DZ  (independent  of  y)    =  —  b  for  normal  case  of 
development  in  the  .presence  of  bromide; 

m        Slope  of  d-log  C  straight  line; 

TTBr     Inverse  bromide  sensitiveness,  or  relative  reduction  potential  by 

.  ,     ,  .  .     ,       (C0)  x . 

bromide  depression  method  =  TT=TT — I — _•      , 

THE  GENERAL  EFFECT  OF  BROMIDE  ON  PLATE  CURVES 

The  normal  effect  of  increasing  the  concentration  of  bromide 
is  shown  in  Fig.  8.  Plates  are  developed  with  and  without 
bromide,  for  varying  times,  producing  different  values  of  y> 
and  a  complete  series  is  obtained  for  no  bromide  and  for  each 
concentration  of  bromide  used.  After  plotting  the  H.  and  D. 

39 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


SID    LOG.E         — *    LOG.E 


-.       -_ 

SHOWN  ARC  FOR     C1  C2          C3 

B2  =  8,+ A  B 
IN  WHICH  CASE  B3  :*J+A   B 


Fig.  8 


curves,  values  of  D  at  the  standard  exposure  are  plotted  against 
the  corresponding  values  of  y.  This  gives  a  D-y  straight 
line  for  each  concentration,  indicating  that  the  straight 
lines  of  each  set  of  plate  curves  meet  in  a  point.  The  co- 
ordinates of  the  point  of  intersection,  a  and  b,  are  determined 
as  outlined  above.  The  effect  of  bromide  is  then  found  to  be 
that  indicated  by  the  figure,  the  intersection  point  undergoing 
a  displacement  downward  along  a  vertical  line.  There  may  be 
deviations  right  and  left  in  the  value  of  a,  but  these  are  usually 
small.  The  general  relations  are  as  follows: 

At  C  =  0  and  b0  =  0,  for  the  unbromided  developer  the 
H.  and  D.  curves  intersect  on  the  log  E  axis; 

At  the  critical  concentration,  C0,  the  intersection  point 
begins  to  move  downward ; 

40 


THE  THEORY  OF  DEVELOPMENT 

d,  the  density  depression  (for  any  concentration  of  potassium 
bromide)    =    —  b,  or  the  lowering  of  the  intersection  point; 
b  is  therefore  a  function  of  the  bromide  concentration 
-b   =  m  (log  C    -  log  C0). 

Consequently,  over  a  range  of  concentrations,  b  increases 
(negatively)  by  the  constant  Ab  if  the  concentration  is 
increased  by  the  same  proportion  each  time;  that  is, 

b,  =  6x+  A  b 
bz  =  b<i  +  A  b 
64  =  63  +  A  6,  etc.,  if 


EXPERIMENTAL  PROOF  OF  THE  COMMON  INTERSECTION 

So  much  of  the  data  can  be  clearly  presented  only  by 
reproducing  the  curves  obtained  (tables  of  data  would  convey 
little  meaning)  that  it  is  impossible  to  give  as  much  as  desired. 
An  attempt  has  been  made  to  avoid  choosing,  consciously  or 
otherwise,  only  those  cases  giving  nearly  ideal  results.  By 
no  means  all  the  results  obtained  are  as  good  as  those  shown, 
but  the  conclusions  throughout  are  based  on  the  general 
average  of  many  examinations. 


LOt.  I 

Fig.  10 

Fig.  9  shows  a  set  of  H.  and  D.  straight  lines  copied  from 
the  original  curves.  The  times  of  development  vary  from 
20  seconds  to  20  minutes.  Seed  23  emulsion  on  patent  plate 
glass  was  used.  The  developer  was  M/20  paraphenylglycine. 
(For  concentration  of  sulphite  and  alkali  and  other  experi- 
mental details  see  Chapter  I.)  Development  was  carried 
out  without  bromide  at  20°  C.  These  curves  illustrate  the 
intersection  point  for  unbromided  development. 

41 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


Fig.  10  gives  the  results  for  the  same  emulsion  under  similar 
conditions,  but  with  M/20  paraminophenol  hydrochloride 
and  0.04  M.  potassium  bromide.  This  result  is  not  so  good  as 
many  obtained. 

It  is  unnecessary  to  consider  the  H.  and  D.  curves  them- 
selves, for  it  has  been  shown  that  the  best  criterion  for  the 
existence  of  the  common  intersection  point  is  the  relation 
between  density  and  gamma.  If  the  latter  represents  a 
straight  line  function  the  curves  meet  in  a  point.  Accordingly 
we  shall  examine  some  representative  D-y  curves. 

If  the  D-y  curve  for  the  results  shown  in  Fig.  9  is  plotted, 
we  get  the  straight  line  in  Fig.  11.  The  fact  that  this  is  a 


Y 
Fig.  11 


Fig.  12 


straight  line  indicates  that  the  lines  meet  in  a  point,  and  the 
fact  that  it  passes  through  the  origin  shows  that  the  lines  meet 
on  the  log  E  axis.  That  is,  in  accordance  with  what  has  been 
said,  if  the  intercept  A  on  the  y  axis  is  equal  to  zero,  b  =  [0. 
Plotting  the  data  from  Fig.  10  in  the  same  way  gives  the 
line  of  Fig.  12.  Here  the  points  of  the  D-y  relation  are 
not  in  so  straight  a  line.  Least-squaring  the  data  for  both 
slope  and  intercept  gives  the  line  shown.  A  has  a  positive 
value.  Since  b  =  —Ad  (equation  4),  b  has  a  real  value, 
indicating,  as  shown  in  Fig.  10,  that  the  H.  and  D.  straight 
lines  meet  in  a  point  below  the  log  E  axis. 


Fig.  13-A 


Fig.  13-B 


42 


THE  THEORY  OF  DEVELOPMENT 


Fig.  13-C 


Fig.  13-D 


Other  examples  are  shown  in  Figs.  13  and  14. 

Fig.  13  represents  cases  of  normal  development  with  no 
bromide  present.  Fig.  13a  gives  results  of  M/20  paramin- 
ophenol  on  Pure  Bromide  Emulsion  I1,  Fig.  13b,  of  M/20 
chlorhydroquinone  on  Pure  Bromide  Emulsion  I;  Fig.  13c, 
of  M/20  paraphenylglycine  on  Pure  Bromide  Emulsion  II1, 
Fig.  13d,  of  M/20  paraminophenol  on  Seed  Process  Emulsion. 

All  examples  shown  in  Fig.  14  have  the  same  log  E. 


Fig.  14-A 


y 
Fig.  14-B 


Fig.  14-C 


Fig.  14-D 


1  Special  experimental  emulsions  made  in  the  laboratory  and  containing  only  bromide 
of  silver  as  the  sensitive  salt. 

43 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


Fig.  140,  M/20  paraminophenol  on  Special  Emulsion  XII, 
no  bromide  in  developer;  Fig.  146,  M/20  paraminophenol  on 
Special  Emulsion  X,  no  bromide  in  developer;  Fig.  14c,  M/20 
paraminophenol  on  Special  Emulsion  XIII,  no  bromide  in 
developer;  Fig.  14 d,  M/20  paraminophenol  on  Special  Emul- 
sion XI,  no  bromide  in  developer. 

Fig.  14a  illustrates  a  special  case  in  which,  because  of  an 
emulsion  effect  which  can  be  explained  in  accordance  with 
present  conceptions,  the  D-y  line  usually  does  not  pass  through 
the  origin.  That  is,  the  H.  and  D.  curves  meet  below  the  log 
E  axis  when  no  bromide  is  used  in  the  developer. 

Many  other  illustrations  could  be  given,  but  the  above  are 
sufficient.  Though  some  experiments  were  not  conclusive, 
there  were  no  cases  of  normal  development  in  which  any  other 
systematic  condition  existed. 

DATA  ON  THE  EFFECT  OF  BROMIDE  ON  THE 
INTERSECTION  POINT 

Density-gamma  curves  were  plotted  for  many  developers 
used  on  different  emulsions  with  varying  concentrations  of 
bromide.  In  general,  these  results  were  in  accord  with  those 
illustrated  here.  As  required  by  the  theory  outlined,  6, 
the  slope  of  the  D-y  line,  is  constant,  and  independent  of 
the  bromide  concentration.  From  equation  3,  a  =  log  E  -  6. 
Since  log  E  is  constant  (unless  otherwise  stated),  a  constancy 
of  9  indicates  a  constancy  of  a.  That  is,  the  intersection 
point  moves  directly  downward  as  b  increases. 

To  prove  this,  the  data  from  the  D-y  relation  were  least- 
squared  for  slope  and  intercept  where  the  straight  lines  could 
not  be  drawn  by  inspection. 

Fig.  15  shows  the  curves  for  M/20  paraminophenol  on  Special 
Pure  Bromide  Emulsion  I,  with  various  concentrations  of 
bromide.  The  slope  of  the  straight  lines  is  nearly  the  same, 
even  at  the  highest  concentration. 


D-Y  curves  for  KBr   concentrations 
0,  .01,  .04,  .08  and  .32  M. 

Fig.  15 


D-T  Curves  for  KBr  concentrations 
0,  .01,  .02,  .04,  .08,  .16  and  .32  M. 


44 


Fig.  16 


THE  THEORY  OF  DEVELOPMENT 

Fig.  16  gives  the  D-y  straight  lines  (obtained  by  least- 
squaring  the  data),  for  M/25  bromhydroquinone  on  Special 
Pure  Bromide  Emulsion  II.  The  various  points  are  not 
indicated  because  the  curves  are  so  close  together  that  the 
many  points  would  be  confusing. 

The  curves  in  Fig.  17,forM/20 
chlorhydroquinone  on  Special 
Pure  Bromide  Emulsion  II,  are 
not  so  good  as  those  generally 
obtained.  The  curves  for  .01 
and  .02  M  potassium  bromide, 
and  for  0.16  and  0.32  M,  lie 
nearer  each  other  than  they 
should. 

Space  does  not  permit  detail- 
ing more  of  these  individual 


Fig.  17 


cases.  However,  one  very  complete  experiment  is  described 
to  illustrate  the  method,  which  fulfills  all  present  requirements. 
This  experiment  was  performed  with  M/20  dimethylparamino- 
phenol  sulphate  on  Seed  30  emulsion  coated  on  patent  plate 
glass.  The  range  of  concentrations  of  bromide  was  from  0.01 
to  0.64  M.  The  data  were  interpreted  as  follows:  The 
D-Y  data  were  plotted  for  each  concentration,  and  the 
observations  least-squared  for  slope  and  intercept.  The 
average  slope  for  all  the  curves  was  then  obtained,  and  the 
observations  again  least-squared  to  the  average  slope  for  the 
value  of  the  intercept  A.  This  is  justifiable  since  a  great 
deal  of  experimental  data  has  indicated  that  the  slope  is 
practically  constant.  The  curves  in  Fig.  18  show  how  well 
the  observations  bear  out  the  conclusions,  and  what  deviations 
there  are  from  the  common  slope.  As  may  be  seen,  deviations 
are  relatively  small.  The  standard  value  of  log  E  used  was 
3.00  (logs  to  base  10  of  relative  exposures).  The  average 
slope,  0,  was  2.78.  Hence  a  =  log  E  -  0,  or  a  =  3.00  - 
2.78  =  0.22  for  all  cases.  The  value  of  A  may  be  seen  from 
the  curves  for  each  concentration ;  and  it  will  be  remembered 
that  6  =  —Ad. 

Analysis  of  all  available  data  has  shown  that  the  normal 
effect  of  bromide  on  the  plate  curves  (H.  and  D.  curves)  is  a 
downward  displacement  of  the  intersection  point. 

Having  now  proved  the  existence  of  the  common  intersection 
and  its  behavior  with  bromide,  we  may  proceed  to  a  study  of 
the  bromide  depression  and  its  applications. 


45 


MONOGRAPHS    ON    THE    THEORY    OF    PHOTOGRAPHY 


Fig.  18-A 


y 
C=.01 

Fig.  18-B 


y 

C=.02 

Fig.  18-C 


C=.04 

Fig.  18- D 


46 


THE  THEORY  OF  DEVELOPMENT 


y 

C=.08 

Fig  18-E- 


> 


C=.16 

Fig.  18-F 


C=.64 

Fig.  18-H 


47 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


THE  EVALUATION  OF  THE  DENSITY  DEPRESSION 

The  density  depression,  d,  may  be  expressed  most  conven- 
iently in  terms  of  the  coordinates  of  the  points  of  intersection 
and  their  relative  shift  due  to  the  bromide  (equation  9, 
Chapter  I) 

d   =    -b   +  bQ  +  (a   —  a0)    Y  , 

where  a  and  b  are  the  coordinates  for  the  bromide  concentra- 
tion C,  and  a0  and  b0  their  values  when  no  bromide  is  used. 
This  is  the  general  equation  which  includes  corrections  for 
deviations  from  the  ideal  case  in  which  a  =  a0,  b0  =  0,  the 
depression  d  =  -b,  and  d  is  therefore  independent  of  y. 

Table  3  gives  an  analysis  of  least-squared  density-gamma 
data  from  earlier  experiments  on  Seed  23  emulsion  (patent 
plate).  These  data  are  much  less  perfect  than  those  from 

TABLE  3 

Seed  23  Emulsion  of  May,  1917 
Analysis  of  Least-squared  Density-gamma  Data 
KBr 


Developer 

2?)  Chlorhydroquinone 

Experiment  14 


M  Monomethyl    par- 
20  aminophenol  sulphate 
Experiment  45 


M    Paraminophenol    hy- 
20  drochloride 
Experiment  37 


M  Hydroquinone 
20 
Experiment  11 


C        log 

E    e 

A 

a 

b 

0       2.30 

1.82 

0 

.48 

-    0 

.01M 

2.30 

.21 

.00 

-    .48 

.02 

2.25 

.29 

.05 

-    .68 

.04 

2.15 

.30 

.15 

-    .65 

.08 

2.64 

.52 

-.34 

-1.37 

.16 

2.20 

.48 

.10 

-1.05 

.32 

2.06 

.50 

.24 

-1.03 

0       2.10 

1.62 

.05 

.48 

-.08 

.01 

1.53 

.09 

.57 

-.14 

.04 

1.82 

.16 

.28 

-.29 

.08 

1.42 

.14 

.68 

-.20 

.16 

1.36 

.15 

.74 

-.20 

.32 

1.23 

.15 

.87 

-.19 

.64 

1.33 

.20 

.77 

-.27 

0       2.40 

1.98 

.06 

.42 

-.12 

.01 

1.74 

.06 

.66 

-.10 

.02 

2.00 

.13 

.40 

-.26 

.04 

2.00 

.20 

.40 

-.40 

.07 

2.08 

.29 

.32 

-.60 

.10 

1.67 

.23 

.73 

-.38 

.20 

3.10 

.43 

-.70 

-1.33 

.40 

data  of 

insufficient 

range. 

0       2.40 

2.24 

.06 

-.16 

-.12 

.005 

2.36 

.15 

.04 

-.35 

.01 

2.45 

.28 

-.05 

-.69 

.02 

2.42 

.34 

-.02 

-.81 

.04 

2.04 

.32 

.36 

-.65 

.10 

2.50 

.60 

-.10 

-1.50 

d 

0 

00 
.22 
.32 
.55 
.67 
.79 

0 

.15 
.00 
.32 
.38 
.50 
.48 

0 

.20 
.12 
.26 
.38 
.57 
.09 


0 

.11 
.36 
.51 
.73 
1.12 


48 


THE  THEORY  OF  DEVELOPMENT 


ao  LOG.wC      85 


later  more  complete  work.  Different  values  of  log  E  were 
used  because  the  straight  line  range  of  the  plate-curve  was  not 
great  enough  to  provide  for  the  varying  conditions  which 
were  obtained,  and  it  was  desirable  to  use  values  of  D  which 
lay  within  the  straight  line  portion  in  all  cases. 

The  deviations  in  6,  and  consequently  in  a,  are  greater 
than  desirable,  and  irregular.  The  density  depression,  d, 
in  the  last  column  is  computed  from  equation  9,  the  formula 
repeated  above,  where  the  value  1.0  is  taken  for  y.  Although 
b0  is  not  equal  to  0  in  each  of  these  cases,  a  general  trend  in 
that  direction  is  indicated. 

Before  proceeding  with  the  de- 
termination of  the  density  de- 
pression, let  us  examine  more 
closely  the  relations  for  the  con- 
stant a.  In  Fig.  19,  a  (as  meas- 
ured from  the  D-j  curves)  is 
plotted  against  the  logarithm  of 
the  bromide  concentration  for 
several  average  cases  These 
and  other  results  show  that  the 
total  deviation  of  a  is  relatively 
small.  It  is  not  necessary  to 
discuss  here  at  greater  length 
the  fact  that  over  a  wide  range 
a  is  independent  of  the  bromide 
concentration  and  a  constant 
for  the  given  plate  and  devel- 
oper. Accordingly  the  density 
depression  is  found  by  means  of 
the  simple  relation  d  =  —b  (b 


Fig.  19 


is  considered  negative,  d  positive).  The  use  of  the  constant  a 
and  the  method  outlined  in  determining  plate  speeds  will  be 
discussed  in  the  next  chapter. 

RELATION     OF     THE     DENSITY     DEPRESSION     TO     THE     BROMIDE 

CONCENTRATION    AND    THE    DEPRESSIONS    WITH    DIFFERENT 

DEVELOPERS 

If  the  density  depression,  d,  is  plotted  against  the  logarithms 
of  the  corresponding  bromide  concentrations,  a  straight  line 
is  obtained,  as  indicated  in  Chapter  I.  The  equation  for 
this  line  may  be  written 

d   =  m  (log  C   -  log  Co), 

m  being  the  slope  and  log  C0  the  intercept  on  the  log  C  axis, 
as  explained  above.  (See  Fig.  14.) 

49 


MONOGRAPHS  ON  THE  THEOEY  OF  PHOTOGRAPHY 

Typical  experimental  results  are  given  in  the  following 
figures.  Fig.  20A  gives  the  results  obtained  with  M/10  ferrous 
oxalate  on  Seed  23  emulsion.  Fig.  20B  represents  the  depres- 
sions for  M/20  paraphenylglycine  on  Seed  30  emulsion. 


Figs.  20-A  and  B 

Not  only  these,  but  practically  all  the  curves  obtained  have 
very  nearly  the  same  slope,  m.  The  general  method  of 
treatment  of  the  data  is  therefore  like  that  of  the  D-y  curves. 
The  d-\og  C  curves  were  obtained  for  each  emulsion  with  all 
the  developers  used  on  that  emulsion,  and  least-squared 
(where  necessary)  for  slope  and  intercept.  The  slopes,  which 
were  very  similar,  were  averaged,  and  the  data  again  least- 
squared  to  the  common  slope  for  the  intercept  log  CV  It 
will  be  seen  that  in  some  cases  there  are  not  many  observations, 
but  it  must  be  remembered  that  each  point  on  the  curves 
represents  much  experimental  work,  sometimes  as  many  as 
fifty  or  sixty  plates,  and  it  was  impossible  at  the  time  when 
some  of  this  work  was  begun  to  foresee  that  so  much  material 
would  be  necessary.  In  some  cases,  therefore,  we  ran  short 
of  the  particular  batch  of  emulsion  or  developer  needed.  The 
deviation  of  observations  based  on  so  many  plates  can  scarcely 
be  explained,  but  they  are  in  accord  with  general  experience 
in  photographic  work.  Fig.  21  gives  data  for  different 
developers  on  Seed  23  emulsion.  The  lines  represent  the 
result  of  least-squaring  to  the  common  slope,  m  =  0.43. 

Fig.  22  illustrates  similar  results  with  Pure  Bromide 
Emulsion  I. 

50 


THE  THEORY  OF  DEVELOPMENT 


Fig.  21 


Fig.  22 


Fig.  23 

In  Fig.  23  are  shown  the  depressions  for  four  developers 
used  on  Seed  30  emulsion.  In  the  second  of  these  experiments, 
at  high  concentrations  of  bromide,  represented  by  Fig.  23b, 
there  is  a  departure  from  the  relations  thus  far  described. 
This  is  also  shown,  though  to  a  less  extent,  by  dimethylpar- 
aminophenol,  in  Fig.  23c,  and  was  noticed  in  other  cases. 
The  phenomena  may  be  due  to  a  change  in  the  photometric 
constant,  (ratio  between  density  and  mass  of  silver  per  unit 
area)  or  to  some  specific  action  of  the  bromide,  a  possibility 
discussed  later,  or,  more  probably,  to  both. 

51 


CHAPTER    III 


Developing  Agents  in  Relation  to  their  Relative 

Reduction  Potentials  and  Photographic 

Properties  (Continued) 

THE  RELATIONS  FOR  THE  SLOPE  OF  THE  DENSITY 
DEPRESSION  CURVES 

The  comparison  of  the  values  of  C0  for  different  developers 
will  be  a  logical  method  only  if  the  slope  m  of  the  density- 
depression  curves  is  constant.  The  evidence  we  have  for  this 
is  shown  in  Table  4.  Some  later  work  has  shown  the  rate  of 
change  of  depression  of  the  maximum  density  or  equilibrium 
value  with  bromide  concentration  to  be  the  same  (i.  e.,  the 
depression  in  maximum  density  expressed  as  a  function  of  the 
bromide  concentration  has  the  same  slope),  so  that  very 
probably  it  is  correct  to  assume  the  slope  constant. 

The  data  in  Table  4  were  least-squared  for  slope  and 
intercept  except  where  otherwise  notecf. 

TABLE  4 

EMULSION  DEVELOPER  m 

Seed  23  of  May,  1917  .  .Bromhydroquinone 20 

Monomethylparaminophenol  sulphate 28 

Toluhydroquinone 52 

Paraminophenol  hydrochloride 36 

Chlorhydroquinone 50 

Hydroquinone .80 

Average 44 

Pure  Bromide  I Hydroquinone 64 

Paraminophenol  hydrochloride .54 

Chlorhydroquinone .  56 

Average 58 

Pure  Bromide  II Bromhydroquinone 28 

Chlorhydroquinone 38 

Paraphenylglycine .  70 

Average 45 

Seed  23  of  June,  1919.  .Ferrous  oxalate 54 

Hydroquinone 98 

Paraphenylglycine 871 

Seed  30  of  July,  19192.  .  Paraphenylglycine 54 

Pyrogallol 42 

Dimethylparaminophenol  sulphate 46 

Paraminophenol  hydrochloride .40 

Average 46 

1  Only  four  depression  values  were  obtained  here,  therefore  the  data  were  not  least 
squared. 

2  Most  complete  data  secured. 

52 


THE  THEORY  OF  DEVELOPMENT 

The  values  in  Table  4  are  of  wide  range  for  averaging.  The 
conclusion  that  the  slope  is  practically  constant  was  reached 
by  weighing  this  and  later  analogous  data,  the  relative  values 
of  which  cannot  be  indicated  in  the  present  table.  In  the 
earlier  work  the  deviations  were  large  because  but  few  dif- 
ferent concentrations  of  bromide  were  employed.  For  the 
most  complete  data  (widest  range  and  greatest  number  of  bro- 
mide concentrations,  and  data  therefore  of  most  weight)  such 
as  the  last  series  of  table  4,  the  values  were  much  more  consist- 
ent. The  averages  for  the  other  series  of  the  table  are  partly 
accidental. 

There  is  a  possibility,  however,  that  hydroquinone  is  an 
exception  to  the  rule,  as  it  persistently  shows  a  higher 
slope.  This  developer  was  found  to  be  somewhat  unusual  in 
other  respects,  possibly  because  of  the  easy  regeneration  of 
the  developing  agent  from  its  oxidation  products  by  the 
action  of  the  other  constituents — a  question  to  be  discussed 
later.  But  until  there  is  proof  to  the  contrary,  it  will  be 
assumed  that  the  slope  of  the  density  depression-bromide 
concentration  function  is  constant. 

It  is  found  also  that  the  slope  m  is  independent  of  the 
emulsion  and  of  the  developer  used.  This  is,  therefore,  one 
of  the  more  fundamental  constants,  and  probably  indicates 
an  important  fact  which  will  be  used  as  a  general  law,  for  the 
present  at  least. 

Since  m  is  constant — that  is,  the  rate  of  change  of  de- 
pression with  bromide  concentration  is  independent  of 
emulsion,  developer,  and  bromide  concentration — a  method 
for  determining  the  relative  bromide  sensitiveness  of  any 
developer  may  be  formulated.  For  any  two  developers, 
a  comparison  of  the  log  C  values  at  which  the  same  depression 
is  produced  will  yield  the  same  results  as  a  comparison  of  the 
intercepts  (log  C0).  Hence,  the  concentrations  of  bromide 
required  to  produce  the  same  depression  or  the  same  change 
in  the  amount  of  work  done  by  any  two  reducing  agents, 
used  under  conditions  described  above,  may  be  computed. 
As  stated  above,  this  method  is  analogous  to  comparisons  of 
physical  forces,  since  the  resistances  required  to  cause  the 
same  change  in  the  amount  of  work  done  have  been  measured. 
It  may  be  assumed  that  these  give  a  measure  of  the  relative 
chemical  potentials  of  any  two  developers,  though,  as  pre- 
viously stated,  this  is  not  necessarily  a  true  indicator  of  the 
relative  chemical  potentials  of  the  isolated  reducing  agents. 
Also,  further  work  will  be  required  to  establish  the  quantitative 
relations  connecting  this  method  with  the  chemical  theory. 

53 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

However,  as  already  stated,  additional  evidence  in  favor  of 
this  method  (see  Chapter  VI)  shows  that  the  rate  of  displace- 
ment of  the  equilibrium  is  the  same  as  that  measured  here, 
and  comparisons  made  on  that  basis  place  developers  in  the 
same  order.  Consequently  it  is  felt  that  this  method  will 
eventually  be  established  as  fundamentally  correct. 

THE  VARIATION  OF  C0    WITH  THE  EMULSION  USED 

Although  m  has  been  found  to  be  independent  of  the  emul- 
sion employed,  this  is  apparently  not  true  of  C0)  the  value  of 
the  concentration  of  bromide  required  for  initial  depression. 
This  is  unfortunate,  as  it  necessitates  the  use  of  one  developer 
as  a  standard  each  time  a  different  emulsion  is  used,  which 
means  a  laborious  re-determination  of  the  density-depression 
curve  for  a  developer  with  which  other  comparisons  have  been 
made.  The  values  of  C0  for  a  given  developer  on  different 
emulsions  are  usually  of  the  same  order,  but  the  deviations  are 
so  great  that  we  must  conclude  for  the  present  that  the  emul- 
sion influences  the  result.  Table  5  gives  the  data  available. 

TABLE  5 
Values  of  C0  (in  units  of  4th  decimal  place,  i.  e.  X  104) 

DEVELOPER  EMULSIONS    USED 

Seed  23  Pure  AgBr  Pure  AgBr   Seed  23         Seed  30 

May,  1917  I  II            June,  1919  July,  1919 

Hydroquinone 10  4.4  ....            20            .... 

Paraminophenol    hydro- 
chloride 69  72.5  25 

Paraphenylglycine 3.4      11.8           42  10 

Chlorhydroquinone 59  35.5  40.8          

Bromhydroquinone 155  ....  186.0          ....           .... 

If  the  values  of  C0  vary  with  the  emulsion,  this  constant 
may  be  of  some  importance  in  expressing  the  characteristics 
of  the  plate.  However,  the  difficulty  of  determining  it 
would  prohibit  its  practical  use. 

THE  VARIATION    OF    C0  WITH  THE  DEVELOPER.       RELATIVE 
REDUCTION  POTENTIAL,     7TBr 

The  greater  the  value  of  C0,  the  lower  the  bromide  sensitive- 
ness of  the  developer.  Hence,  we  may  say  that 

Bromide  sensitiveness  <*  — -. 

£"0 

But  the  greater  the  value  of  C0  the  greater  the  reduction 
potential.  Therefore, 

•^Br    =  /  (C0),  which  is  possibly  7rBr    =  k  log  C0. 

54 


THE  THEORY  OF  DEVELOPMENT 


But  for  the  time  being  we  arbitrarily  define  this  as 


Br 


=    k  C 


0. 


At  present  there  is  no  means  for  determining  this 
constant  k.  As  stated  above,  it  is  impossible  with  our 
present  knowledge  to  measure  the  absolute  chemical 
potential.  The  reduction  potential  of  a  developer  X  will 
be  (TT  Br)  x  =  k  (C0)  x;  that  for  a  given  standard  developer 
will  be  (TT  Br)  Std  =  k  (C0)  std.  Consequently  the  relative 
reduction  potential,  ^Br,  for  any  developer  X  referred  to  a 
given  standard  is 

7TB      =       (^Br)    x          =       k   (C0)    x  =  (Co)    x       . 

(^Br)   Std.  k   (C0)   Std.  (C0)    Std. 

This  relation  has  been  used  for  obtaining  the  new  data  by 
this  method.  The  results  are  given  in  Table  6.  Values  of 
C0  are  expressed  in  units  of  the  fourth  decimal  place  (molar 
concentrations  of  potassium  bromide).  ^Br  is  relative  to 
the  standard  developer  indicated.  All  values  of  T^BF  are 
referred  to  M/20  hydroquinone  as  having  a  reduction  potential 
of  unity.  It  should  be  remembered  that  all  the  developers 
(except  bromhydroquinone  and  ferrous  oxalate,  which  were 
used  in  concentrations  of  M/25  and  M/10,  respectively), 
are  twentieth  molar,  with  50  gm.  sodium  sulphite  +  50  gm. 
sodium  carbonate,  per  liter. 

TABLE  6 

Values  C0  and 


Q  TT      -°        . 

EMULSION  (  C0)  Std. 

Seed  23  of  May,  1917  — 

Paraphenylglycine  ....................  3  0.3 

Hydroquinone  ........................  10  1.0  Std. 

Toluhydroquinone  ....................  25  2.5 

Chlorhydroquinone  ....................  60  6.0- 

Paraminophenol  hydrochloride  .........  70  7.0 

M/25  Bromhydroquinone  ..............  160  16.0 

M/20  Monomethylparaminophenol 

sulphate  ...........................  200  20.0 

Pure  Bromide  I  — 

Hydroquinone  ........................  4.4  1.0  Std. 

Paraminophenol  hydrochloride  ..........  73  16.5  Small  amount 

of  data 

Chlorhydroquinone  ...................  36  8.1- 

55 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Pure  Bromide  II — 

Paraphenylglycine 12          1.7 

Chlorhydroquinone 41         6.0  (Assumed  Std. 

and  =  6.0 
as  on  Seed 
23) 

M/25  Bromhydroquinone 186       26.8 

Seed  23  of  June,  1919— 

M/10  Ferrous  oxalate 8         0.3 

M/20  Hydroquinone 25          1.0  Std. 

M/20  Paraphenylglycine 40          1.6 

Seed  30  of  July,  1919— Most  complete  data— 

Paraphenylglycine 10          1.6  Std. 

Paraminophenol  hydrochloride 25         5 

Dimethylparaminophenol  sulphate 60       10 

Pyrogallol 100       16 

A  study  of  Table  6  shows  that  it  is  extremely  difficult  to 
reproduce  actual  numerical  values  of  T^BI--  For  example, 
the  following  were  obtained  for  paraminophenol  used  on  three 
emulsions: 

Seed  23  of  May,  1917 7 

Pure  Bromide 16.5 

Seed  30.. 5 

Values  for  paraphenylglycine  vary  as  follows: 

Seed  23  of  May,  1917 0.3      . 

Pure  Bromide  II 1.7 

Seed  23  June,  1919 1.6 

Seed  30  July,  1919. 1.6 

However,  with  the  one  exception  of  paraphenylglycine  on 
Seed  23  emulsion  of  May,  1917,  the  developers  always  fall  in 
the  same  order.  We,  therefore,  weigh  the  data  as  fairly 
as  possible,  and  adopt  the  result  as  the  best  we  can,  with 
no  great  claims  for  accuracy.  With  paraphenylglycine,  for 
Instance,  the  value  0.3  is  obtained  with  only  three  concentra- 
tions. The  data  for  the  other  emulsions,  especially  for  the 
last,  are  more  complete.  The  evidence  in  any  case  is  three  to 
one  in  favor  of  the  higher  value.  Proceeding  in  this  manner 
we  can  construct  a  table  of  what  we  consider  to  be  the  fairest 
approximations  to  the  relative  reduction  potentials.  This 
table,  including  some  of  the  results  of  previous  work,  is  given 
below. 

TABLE  7  ^Br 

Hydroquinone 1.0 

Paraphenylglycine 1.6 

Toluhydroquinone 2.2 

Paraminophenol 6 

Chlorhydroquinone 7 

Dimethylparaminophenol 10 

Pyrogallol - 16 

Monomethylparaminophenol 20 

Bromhydroquinone 21 

Methylparamino-orthocresol 23 

56 


THE  THEORY  OF  DEVELOPMENT 


PREVIOUS  RESULTS 


Measurements  of  reduction  potentials  made  prior  to  those 
recorded  above  are  given  in  Table  8. 


TABLE  8 

REDUCTION  POTENTIAL  VALUES 

From  Work  done  Prior  to  1917 
Sheppard  (Photographic  Method) —  ^Br 

M  / 10  Hydroquinone  (caustic) 1.0 

M/10  Ferrous  oxalate 1.8 

M/10  Hydroxylamine  hydrochloride 2.0 

M/10  Paraminophenol  hydrochloride  (caustic) 5.4 

Frary  and  Nietz  (Electrometric  Method)  — 

Hydroquinone  (Sod.  carb.) 1.0 

Mixture  of  hydroquinone  and  monomethylparaminophenol  sul- 
phate     2.7 

Diamidophenol 36.0 

Thiocarbamide 53  . 0 

Nietz  (Preliminary  work,  this  laboratory)  (Photographic  Method)  — 

M  /20  Paraphenylglycine 0.7 

M/20  Hydroquinone 1.0 

M/20  Chlorhydroquinone 1.4 

M /20  Toluhydroquinone 1.8 

M/20  Paraminophenol 2.7 

M/20  Monomethylparaminophenol 7  to  16 

M/20  Paraphenylene  diamine — no  alkali 0.3 

M/20  Paraphenylene  diamine — with  alkali 0.4 

M/20  Methylparaphenylene  diamine — no  alkali 0.7 

M/20  Methylparaphenylene  diamine — with  alkali 3.5 

M/20  Methylparamino-orthocresol 23 

M/20  Paramino-orthocresol 7 

Sheppard's  results,  recomputed  to  a  basis  of  hydroquinone 
=  1.0,  were  corrected  for  the  reduction  equivalent,  or 
"reducing  power."  Sheppard  found,  as  did  also  the  writer, 
that  hydroquinone  had  certain  marked  characteristics,  not 
yielding,  by  the  former's  method,  a  constant  value  for  the 
relative  reduction  potential.  The  joint  work  of  Frary  and 
the  writer  was  of  a  preliminary  nature,  and  was  unfortunately 
not  carried  out  with  standard  concentrations  of  the  developers. 
But  the  values  obtained  are  apparently  in  the  proper  order 
and  useful  as  an  indication  of  the  relations. 

The  values  given  in  the  third  section  of  the  table  were 
obtained  by  the  writer  by  the  use  of  Sheppard's  method. 
These  are  not  as  accurate  as  later  work,  but  again  the  results 
are  in  the  same  order. 

57 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


AN  ENERGY  SCALE  OF  DEVELOPERS 

As  a  result  of  the  measurements  recorded  here,  we  may 
now  state  the  general  order,  on  a  scale  of  developing  energy, 
of  a  number  of  developers.  Including  the  averaged  and 
weighted  results  obtained  from  Table  6,  and  the  general  results 
from  Table  7,  we  may  write  this  "scale  of  developers"  as 
in  Table  9. 

TABLE  9 

^Br 

M/10  Ferrous  oxalate 0.3 

M/20  Paraphenylene  diamine  hydrochloride,  no  alkali 0.3 

M/20  Paraphenylene  diamine  hydrochloride,  plus  alkali 0.4 

M/20  Methylparaphenylene  diamine  hydrochloride,  no  alkali 0.7 

M  /20  Hydroquinone 1.0 

M/20  Paraphenylglycine 1.6 

M/10  Hydroxylamine  hydrochloride 2.0 

M  /20  Toluhydroquinone 2.2 

M/20  Methylparaphenylene  diamine  hydrochloride,  plus  alkali.  ...  3.5 

M/20  Paraminophenol  hydrochloride 6.0 

M/20  Chlorhydroquinone 7.0 

M/20  Paramino-orthocresol 7.0 

M/20  Dimethylparaminophenol  sulphate 10.0 

M/20  Pyrogallol. . .  , 16.0 

M/20  Monomethylparaminophenol  sulphate 20.0 

M/25  Bromhydroquinone 21.0 

M/20  Methylparamino-orthocresol 23  . 0 

M/20  Diaminophenol 30to40 

M/20  Thiocarbamide 50.0 

Further  information  on  reduction  potentials  is  obtained 
by  the  application,  made  later,  of  the  study  of  the  velocity 
curves  and  the  final  or  equilibrium  value  for  the  density. 
A  discussion  of  reduction  potential  and  its  relation  to  photo- 
graphic properties  and  to  the  chemical  constitution  of  the 
developing  agent  is  necessarily  deferred  until  the  collected 
results  are  given. 


58 


CHAPTER  IV 

A  Method  of  Determining  the  Speed  of 

Emulsions  and  Some  Factors 

Influencing  Speed 

The  so-called  "speed"  of  a  photographic  emulsion  is  a 
subject  which  has  played  a  most  important  part  in  the  history 
of  photography.  In  fact  we  may  almost  say  that  it  has  been 
largely  responsible  for  the  scientific  development  of  photog- 
raphy, since  some  of  the  most  important  researches  in  which 
the  principles  of  chemistry,  physics  and  mathematics  have 
been  applied  grew  out  of  an  endeavor  to  obtain  measurements 
of  plate  speeds.  This  is  particularly  true  of  the  well-known 
work  of  Hurter  and  Driffield.  Many  controversies  arose 
following  the  appearance  of  Hurter  and  Drimeld's  first  paper, 
many  of  the  discussions  centering  around  the  determination  of 
emulsion  speed.  Investigation  of  the  subject  is  still  being 
actively  pursued  by  workers  in  the  field  of  sensitometry. 

Special  mention  is  made  of  the  subject  here  because  of  its 
historical  importance  and  because  it  is  hoped  that  the  data 
made  available  by  the  present  work  may  be  of  use  in  studying 
the  many  unsolved  questions  related  to  emulsion  speed. 

IMPORTANCE  OF  THE  METHOD  OF  EXPOSURE 

It  is  to  be  noted  especially  that  while  most  of  the  principles 
already  stated  may  be  applied  to  a  study  of  photographic 
development  irrespective  of  how  the  exposures  are  made 
(so  long  as  they  are  made  always  in  the  same  way),  it  now 
becomes  necessary  to  take  into  account  the  method  of  expo- 
sure. Because  of  the  failure  of  the  plate  to  integrate  properly 
intermittent  exposures,  and  the  failure  of  the  so-called 
"reciprocity  law"  (E  =  //),  both  of  which  may  be  different  for 
different  emulsions,  and  even  for  different  batches  of  the  same 
emulsion,  the  comparison  of  two  emulsions  for  the  exposures 
required  to  give  a  definite  result  involves  considerable  care 
and  knowledge.  The  questions  of  intermittency  effect  and 
reciprocity  failure  are  under  investigation.  The  general 
results  have  shown  that  a  non-intermittent  exposure  on  a  time 
scale  with  proper  adjustment  between  intensity  and  time,  or, 
better  still,  exposure  on  an  intensity  scale  with  a  proper  value 
for  the  intensity,  is  required.  An  intermittent  (rotating 
sector-wheel)  sensitometer  will  give  results  approaching  those 

59 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

of  the  non-intermittent  instrument  as  the  speed  of  revolution 
falls  below  a  certain  value  and  is  gradually  decreased  to  one 
revolution  for  the  entire  exposure.  This  fact  should  be  borne 
in  mind  in  comparing  the  relative  speeds  shown  by  two  emul- 
sions where  the  exposures  are  on  an  intensity  scale  and  the 
time  is  relatively  short. 

DEFINITIONS  AND  SENSITOMETRIC  CONCEPTIONS  INVOLVED 

It  is  obvious  that  according  to  any  conception  of  speed, 
the  shorter  the  exposure  required  to  give  a  definite  result, 
the  greater  the  speed.  If  we  term  H  the  speed 

H  cc   -I  or   H   =  ~. 

It  is  evident  that  this  "definite  result"  should  be  standard- 
ized as  regards  the  method  for  obtaining  the  speed,  the  value 
of  k,  and  the  units  in  which  to  express  E. 

A  clear  conception  of  the  meaning  of  emulsion  speed  was 
first  presented  by  Hurter  and  Driffield.  If  any  two  plates 
are  always  developed  (with  any  developer)  to  a  normal  con- 
trast (as  is  often  done  in  practice) — that  is,  to  a  standard  value 
of  y  —  the  relative  speeds  of  the  two  plates  are  to  each  other 
inversely  as  the  exposures  corresponding  to  their  inertia 
points.  (Reference  to  the  contrast  is  necessary  if  all  cases  are 
to  be  covered.)  This  is  made  somewhat  clearer  by  considera- 
tion of  Fig.  24  and  the  explanation  following. 

If  plates  I  and  II  are  exposed 
in  a  sensitometer,  developed  to 
the  same  degree,  and  their 
densities  measured  and  plotted 
against  the  logarithms  of  the 
corresponding  exposures,  curves 
having  certain  straight  line  por- 
tions, like  I  and  II  in  Fig.  24, 
are  obtained.  If  the  straight 
lines  are  extended  they  cut  the 
log  E  axis  at  log  i\  and  log  i2, 
which  are  termed  the  inertia 

points.  Speed  is  interpreted  as  the  measure  obtained  from 
values  of  the  exposure  required  to  give  a  definite  density. 
Accordingly,  choose  any  ordinary  value  of  density  lying  in  the 
"region  of  correct  exposure"  or  straight  line  of  the  plate,  such 
as  Dstd.  in  the  figure.  Projecting  a  line  parallel  to  the  log  E 
axis  from  Dstd.  to  curves  I  and  II  and  from  the  intersections 


Fig.  24 


60 


THE  THEORY  OF  DEVELOPMENT 

vertically  downward  to  the  log  E  axis  gives  the  points  log  Ei 
and  log  jE2.  Logs  Ei  and  E2  are,  therefore,  the  exposures 
required  to  give  the  same  density  on  plates  I  and  II  under 
these  conditions.  Therefore,  according  to  the  equation 

k 

H  =  —  ,  the  speed  of  one  emulsion  compared  with  the  other 
h, 

is  given  by 


But  since  I  and  II  are  parallel  lines  (plates  at  the  same  degree 

EI  .  i2 

of  development)  the  ratio  —  is  the  same  as  —  ;  or,  the  speed 

rL\  i\ 

relations  can  be  obtained  from  the  values  for  the  inertias. 

TT 

Hence  we  may  write  —  r  =    -A     Further,  if  log  ii  and  log  it 

Hz         i\ 
remain  constant  with  increasing  development,  then  the  ratio 

—  is  not  affected  by  development;  that  is,  the  speed  is  inde- 

i\ 

pendent  of  y. 

Unfortunately,  the  inertia  is  not  always  independent  of  the 
degree  of  development,  especially  if  bromide  is  used  in  the 
developer;  and  it  is  here  that  the  results  described  in  the  pre- 
ceding chapters  may  be  applied. 

We  may  get  rid  of  comparisons  and  relative  speed  values 
by  deciding  in  what  units  to  express  i  and  what  value  to 
assign  to  the  constant  k  in  the  equation 

/p 

H   =  —  (by  definition  of  absolute  speed).  (12) 

Although  E  and  i  have  always  been  measured  in  visual  units, 
there  is  obviously  no  logic  in  such  a  procedure,  since  the 
visual  measurement  of  light  intensity  is  affected  by  limitations 
of  the  human  eye  quite  different  from  those  affecting  the 
photographic  emulsion.  In  other  words,  the  photographic 
plate  does  not  necessarily  see  two  intensities  in  the  same 
relation  as  does  the  human  eye.  However,  until  there  has 
been  put  forward  a  satisfactory  photographic  light  unit,  we 
must  continue  to  use  the  visual  unit,  E  and  i  being  expressed 
in  candle-meter-seconds  (or,  as  commonly  written,  c.  m.  s.)« 
Usually  k  is  so  evaluated  as  to  give  values  of  H  in  convenient 
numbers.  The  value  k  =  34  was  selected  by  Hurter  and  Drif- 
field,  adjusted  for  use  with  their  "Actinograph"  or  exposure 
calculating  scale. 

61 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

All  further  considerations  in  this  monograph  avoid  the 
use  of  absolute  speed  values  in  arbitrary  units.  We  may 
proceed  very  satisfactorily  by  employing  a  relative  exposure 
scale,  this  being  convertible  at  any  time  by  knowing  the  rela- 
tion between  the  scale  and  the  actual  intensity-time  measure- 
ments. For  example,  all  exposures  made  during  the  course 
of  this  work,  beginning  in  February,  1919,  were  such  that 
log  E  =  2.4  represents  1.4  candle -meter-seconds  (visual)  of 
acetylene  screened  with  Wratten  No.  79  filter  to  daylight 
quality.  This  fact  furnishes  the  connecting  link  between  the 
relative  and  absolute  exposure  values. 


A  NEW  METHOD 

The  details  of  a  somewhat  different  method  for  the 
determination  of  definite  sensitometric  constants  expressing 
the  speed  of  an  emulsion  have  already  been  described.  It 
is  for  the  purpose  of  emphasizing  this  method  in  its  affiliation 
to  the  whole  subject  of  speed  that  it  is  taken  up  again.  The 
writer  also  wishes  to  point  out  that  the  older  method,  as 
presented  in  the  foregoing  section,  serves  very  well  in  ordinary 
cases  where  a  good  standard  developer  can  be  used  on  emul- 
sions of  the  usual  type.  But  in  order  to  obtain  a  fair  estimate 
of  speed  in  practically  every  case,  no  matter  what  the  emulsion 
or  the  developer,  other  conceptions  are  most  emphatically 
necessary.  Much  of  the  controversy  on  the  question  has 
arisen  from  the  erratic  results  obtained  in  certain  cases. 

It  has  been  shown  that  the  straight  lines  of  the  H.  and  D. 
curves  for  any  case  of  normal  development  always  have  a 
common  intersection.  The  coordinates  of  this  point  of  in- 
tersection were  termed  a  and  b,  and  these  are  the  sensitom- 
etric constants  with  which  we  are  principally  concerned  here. 
a  is  the  log  E  coordinate  of  this  point  and  b  the  density  coor- 
dinate. If  b  =  0,  the  curves  intersect  on  the  log  E  axis.  This 
is  the  case  for  nearly  every  ordinary  emulsion  and  every 
developer  of  the  usual  type  which  contains  no  bromide. 
But  if  emulsion  or  developer  contain  bromide,  b  has  a  real 
value  and  the  intersection  point  lies  below  the  log  E  axis.  In 
consequence,  log  i  changes  with  time  of  development  and  with 
contrast.  Now  a  is  not  affected  by  bromide,  and  therefore  can 
be  determined  with  any  concentration  of  bromide  (over  a 
wide  range)  in  the  developer.  It  has  been  assumed  that  for 
no  bromide  b  will  be  zero.  Exceptions  to  these  rules  are  rare 
in  the  case  of  ordinary  materials  and  can  be  explained  either 
by  the  fog  error  or  by  a  progressive  secondary  reaction 

62 


THE  THEORY  OF  DEVELOPMENT 


during  development,  which  produces  a  shifting  equilibrium 
point.  Any  case  of  general  deposition  of  silver  over  the  plate 
of  course  upsets  the  relations. 

The  application  of  the  method  to  the  most  general  case  is 
illustrated  in  Fig.  25. 


<  -  LOG.E 


Fig.  25 


Consider  first  a  comparison  in  speed  of  two  emulsions,  I  and 
II.  Different  times  of  development  (under  constant 
conditions)  yield  for  emulsion  I  a  family  of  H.  and  D.  curves 
whose  straight  lines  intersect  in  the  point  Q.  Q  has  coordin- 
ates ai  and  bi,  as  shown.  Similarly  emulsion  II  gives  curves 
intersecting  in  N,  of  which  the  coordinates  are  a2  and  b2. 
Compare  the  two  emulsions  at  any  value  for  the  contrast,  y. 

63 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

The  curves  under  consideration  will  be,  for  example,  those 
marked  I  and  II,  both  at  the  same  Y-  For  this  particular 
value  of  Y  the  exposures  required  to  give  a  standard  density 
(D$td.)  are  Ei  and  EZ,  which  will  be  in  the  same  ratio  as  i\ 
and  iz-  But  if  another  value  for  the  Y  of  the  two  emulsions 
is  chosen,  the  ratio  will  change;  and  if  the  two  plates  are 
not  at  the  same  Y  the  relative  speeds  can  not  be  determined 
at  all  except  under  the  particular  conditions  chosen.  In 
either  case  the  value  obtained  is  not  constant  and  does  not 
express  any  characteristic  of  the  plates.  This  is  precisely 
where  the  old  method  fails,  and  on  such  points  much  time  and 
discussion  have  been  wasted. 

The  constants  a  and  b  are  fundamental  characteristics  of 
the  two  emulsions  for  the  given  developer,  and  the  speed 
relations  may  be  expressed  in  terms  of  them,  as  detailed  below. 

TJ  T? 

2     =          — ^ — .  (from  above) 


TJ  77  ' 

-fi  2  At/i  v\ 

TJ  Tf 

log  -~-  =    log  -j^-  =  log  EZ  —  log  EI  =  log  iz  —  log  ii  =   MN 

=  BN-BM  BN  =  az  BM   =  a,  -MR. 

But,   -~£  =  tan   a  =  Y-  Hence,  MR  = — —  =  -    — 2.  (positive) 


TT  i       HI  EZ  bi  —  bz  /*  o\ 

Hence,  log  —  =   log  —  =  a2  -  at — .  (13) 

t±i  Ei  Y 

This  expression  holds  for  any  value  of  Y-  It  shows  that  in 
such  cases  the  relative  speeds  of  the  emulsion  depend  on  Y  > 
and  the  relations  are  such  that  when  bz  >  bi  (negatively) 
the  speed  of  II  compared  with  I  increases  with  increase  of  Y  ; 
when  bz  <  bi  the  speed  of  II  compared  with  I  decreases  with 
increase  of  Y  •  If  either  bl  or  b2  equals  zero,  the  expression 
simplifies.  If  both  bi  and  bz  equal  zero,  then  the  relative 
plate  speeds  are  defined  by  a2  and  av.  That  is, 

1  HI  ,  EZ  ,  I'i  ,  1  . 

log  —  =    log—  =  log— =    log   iz    -   log   ^1    =    az    -    ai, 
HZ  rL\  ^l 

a2  being  identical  with  log  iz  and  di  with  log  i\.  Thus  we 
have  the  original  Hurter  and  DrifBeld  relation.  Therefore 
the  latter  holds  only  if  the  intersection  points  for  the  two 
families  of  curves  lie  on  the  log  E  axis,  as  Hurter  and  Driffield 
pointed  out.  In  this  case  only  is  the  emulsion  speed  inde- 
pendent of  the  contrast. 

64 


THE  THEORY  OF  DEVELOPMENT 

Now  in  the  case  of  a  single  emulsion,  say  emulsion  I  in 
the  figure,  if  b  has  any  considerable  value  the  absolute  speed 
of  the  plate  increases  with  y.  In  the  case  of  curves  I  and  la, 
for  example,  the  inertia  decreases  from  ii  to  iia  and  the  speed 

k  k 

increases  from  H  =  —  to  //    =    r1-      This    is   better   shown 

1 1  ?ia 

by  the  following:  i 

log  H   =  log  —    =  log  k   -  log  ii. 
ii 

From  the  figure  . : =  y  ,  and  log  ii  =     a (14) 

log*!  —  a  y 

Consequently  log  H  =  log  k  —  a  + — .  (15) 

Hence,  the  lower  the  value  of  a,  the  greater  the  speed;  the 
greater  the  absolute  value  of  b,  the  less  the  speed;  and  the 
greater  the  value  of  y,  the  greater  the  speed  (for  a  given 
value  of  b).  If  b  =  0,  we  have  log  H  =  log  k  -  a,  and  the 
speed  is  independent  of  gamma. 

We  may  define  the  absolute  speed,  in  a  purely  arbitrary 
but  general  way,  as  inversely  proportional  to  that  exposure 
in  visual  meter-candle-seconds  (of  light  from  a  definite  source, 
such  as  screened  acetylene)  which  is  required  to  initiate  the 
deposition  of  silver,  assuming  that  the  emulsion  is  developed 
to  a  gamma  of  unity  and  that  the  H.  and  D.  curve  consists 
entirely  of  a  straight  line.  Practically,  this  is  not  so  complex 
as  it  sounds.  Referring  to  the  figure,  curve  for  emulsion  I, 

k 
for  example,  we  simply  state  that  H  =   - —  where  i  is  the  value 

at  y  =  unity  and  expressed  preferably  in  terms  of  a  and  b, 
and  in  the  proper  units.  From  the  figure  it  may  be  seen  that 
at  y  =  1.0,  log/  =  a  -  b.  This  is  evident  also  from  equation 
14.  Consequently,  to  fit  the  definition 

log  H   =  log  k   -  a   +  b.  (16) 

On  this  basis  the  relations  for  speeds  between  emulsions 
will  be  the  same  as  if  we  chose  densities  actually  on  the 
straight  line  portions  of  the  plate  curves  (so  long  as  both  the 
emulsions  are  at  a  gamma  of  unity).  The  arbitrary  selection 
of  the  speed  ratio  at  a  particular  value  of  y  is  necessary  if 
any  definite  speed  number  is  to  be  assigned  to  an  emulsion 
having  a  real  value  of  b  (and  there  are  such  emulsions).  It 
should  be  clear  from  the  above  that  for  this  case  the  speed 
value  obtained  varies  with  the  contrast.  To  eliminate 
contrast,  therefore,  the  constants  a  and  b  are  determined  and 

65 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

the  speed  number  expressed  by  the  use  of  equation  16.  When 
b  is  zero  the  method  is  as  simple  as  the  older  one,  and  it  may 
be  made  more  precise. 

Therefore,  our  conclusions  are  that  a  and  b  are  the 
sensitometric  constants  desired,  and  that  the  use  of  i  as  a 
characteristic  constant  should  be  abandoned.  Further,  we 
find  it  possible  to  express  the  correct  relations  for  the  speed 
in  terms  of  a  and  b,  whether  or  not  the  speed  is  independent  of 
the  contrast. 

For  the  experimental  method  of  determining  the  constants 
a  and  b  the  reader  is  referred  to  Chapter  I.  In  practice, 
for  the  purpose  of  speed  measurements,  it  is  sufficient  to 
develop  five  pairs  of  plates  for  varying  times  and  to  plot  the 
H.  and  D.  and  the  D-  y  curves  for  the  standard  exposure. 
a  and  b  are  computed  from  the  latter. 

DATA  ON  EMULSION  SPEEDS  AND  THE  VARIATION   OF  SPEED 
1.    VARIATION  OF  SPEED  WITH  EMULSION 

The  above  conclusions  were  reached  from  examination  of 
data  from  thousands  of  plates,  about  thirty  different  develop- 
ing agents  and  fifteen  different  emulsions  being  used.  The 
following  typical  cases  are  sufficient  for  illustration.  Table 
10  gives  results  for  eight  emulsions,  each  developed  in  three 
developers.  Values  of  a,  b,  and  H  are  given.  H  is  found 
from  equation  16  by  assigning  the  value  100  to  k  and  expressing 
a  in  units  of  the  logarithms  of  relative  exposures.  Hence 
equation  16  becomes  log  H  =2  -a  -i-  b.  This  expresses 
speed  values  (on  an  arbitrary  scale)  which  are  independent  of 
y  when  b  =  0,  and  apply  only  for  y  =  1.0  when  b  has  a  real 
value.  Since  in  most  cases  b  =  0,  they  may  be  considered  to 
be  parallel  to  the  H.  and  D.  speed  numbers. 

A  great  deal  of  data  like  those  in  Table  10  was  obtained 
incidentally  to  other  work.  Owing  to  occasional  difficulties 
in  obtaining  consistent  and  uniform  results  with  certain 
developer  and  emulsion  combinations  no  great  precision  could 
be  obtained.  However,  it  was  demonstrated  that,  by  the  use 
of  a  suitable  standard  developer,  a  very  satisfactory  degree  of 
precision  and  reproducibility  in  comparing  emulsion  speeds 
may  be  obtained  by  this  method.  The  personal  error  is 
eliminated  to  a  great  extent,  and  the  information  obtained, 
especially  if  the  emulsion  under  consideration  does  not  behave 
in  the  normal  way,  is  of  more  value  than  that  obtained  by 
the  Hurter  and  Driffield  method,  where,  as  a  rule,  the  inertia 
point  is  obtained  from  two  plates. 

66 


THE  THEORY  OF  DEVELOPMENT 


TABLE  10 

SPEED  OF  PLATES 


Emulsion  Used 

M/20  Paramino- 
phenol  hydro- 
chloride 
(R  340.15) 

M/20  Dimethyl 
paraminophe- 
nol  sulphate 
(R  354.1) 

M/20  Pyrogallol 
(R43.25) 

a 

.14 
1.34 
1.18 
.58 
1.99 
1.74 
1.24 

1.10 
.12 

b 

-.17 
0 
0 

-.22 
0 
-.21 
-.25 

0 
0 

H 

49 
4.6 
6.6 
16 
1 
1.1 
2.1 

8 
76 

a 

.50 
1.66 

6!  73 
2.00 
1.68 

.88 
-.32 

b 

0 
0 

-'l4 
0 

-.25 

0 
0 

H 

32 

2.2 

is'.  5 
1 

1.2 

13 
210 

a 

.14 
1.42 

".50 

1.72 
1.65 
1.54 

-'88 

b 

.04 
0 

0 
0 
-.24 
-.12 

0 

H 

80 
3.8 

32" 
1.9 
1.3 

2.2 

760 

Special  Emulsion  IX.  . 
Special  Emulsion  VIII. 
Special  Emulsion  XI  .  . 
Special  Emulsion  XII  . 
Pure  Bromide  III  

Special  Emulsion  XIII. 
Special  Bromide  XIV.  . 
Film  Special  Emulsion 
XV  .  
Emulsion  3533  

Table  10  shows  that  there  is  an  increase  in  speed  when 
pyrogallol  is  used,  and  that  paraminophenol  increases  the 
speed  to  a  somewhat  greater  extent  than  dimethylparamin- 
ophenol,  The  effect  of  the  developer  is  considered  below. 
The  Special  Bromide  Emulsion  XIV,  which  contains  some 
free  bromide,  persistently  shows  a  real  value  for  b.  This 
may  be  interpreted  in  the  light  of  what  was  said  in  the  second 
chapter  concerning  the  effect  of  bromide  on  the  intersection 
point,  — i.  e.,  on  the  values  of  a  and  b.  It  was  shown  that 
normally,  when  no  bromide  is  present,  b  =  0,  but  with  increas- 
ing concentration  of  bromide  b  assumes  a  real  value  and 
increases,  or  the  intersection  point  moves  downward,  a  is 
not  affected.  Consequently  we  may  infer  that  if  an  emulsion 
shows  a  real  value  of  b,  it  contains  some  free  bromide,  as  we 
do  not  know  of  any  other  explanation  of  this  result.  The 
bromide  may  be  held  by  adsorption  or  inclusion  but  must  be 
present  when  development  takes  place.  Further,  according 
to  earlier  theories,  the  depression  of  the  intersection  point 
(the  value  of  b),  for  a  given  concentration  of  bromide  in  the 
emulsion  is  less  the  greater  the  reduction  potential  of  the 
developer.  Pyrogallol  has  the  highest  reduction  potential 
of  the  three  developers,  and  in  three  out  of  four  cases  showing 
a  real  value  of  b,  the  latter  is  smallest  with  pyrogallol;  that  is, 
in  these  three  experiments  the  free  bromide  in  the  emulsion 
has  the  least  effect  when  pyrogallol  is  used.  The  presence 
of  free  bromide  in  the  emulsion  can  not  be  considered  detri- 
mental, provided  the  depression  produced  is  not  too  large. 

67 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

The  above  explanation  may  account  for  various  effects 
observed  with  certain  developers  and  emulsions.  Hydro- 
quinone  without  bromide,  for  example,  often  shows  a  shift  or 
"regression"  of  the  inertia  point.  Hydroquinone,  having  a 
low  reduction  potential,  and  being  therefore  very  sensitive  to 
bromide,  may  be  affected  by  an  amount  of  free  bromide  in 
the  emulsion  so  small  that  it  has  no  effect  on  other  developers. 
The  foregoing  facts  may  also  account  for  the  successful  use  of 
pyrogallol  in  speed  determinations.  This  does  not  imply 
that  other  developing  agents  will  not  do  as  well,  but  it  is  true 
that  many  developers  whose  reduction  potential  is  as  great  or 
greater  than  that  of  pyrogallol  give  much  more  fog,  thereby 
vitiating  the  results. 

That  some  slow  emulsions  show  a  considerable  value  for  b 
also  partially  accounts  for  the  fact  that  these  emulsions  are 
relatively  faster  when  developed  to  high  gammas.  However, 
this  phenomenon  may  be  explained  partly  by  other  sensito- 
metric  considerations. 

2.  EFFECT  OF  BROMIDE  ON  SPEED 

If  certain  developers  (of  low  reduction  potential)  containing 
an  appreciable  amount  of  bromide  are  used,  the  actual  effective 
speed  of  the  plate  is  reduced  because  of  the  depression  in 
density  produced  by  the  free  bromide  in  the  developer.  The 
extent  of  this  effect  is,  of  course,  measured  by  the  effect  on  b, 
as  shown  by  equation  16 — 

log  H   =  log  k   —  a   -f  b. 

Although  the  question  of  the  advantages  and  disadvantages  of 
the  use  of  bromide  has  been  debated  again  and  again,  we  may 
now  state  with  a  reasonable  degree  of  certainty  that  there  is  a 
real  advantage  in  the  intelligent  use  of  bromide  in  the 
developer.  To  present  this  point  properly  would  require  a 
separate  paper  and  the  use  of  results  not  yet  explained. 
However,  the  following  facts  may  be  presented: 

As  a  rule,  the  fogging  propensity  of  a  developer  is  not 
connected  with  its  reduction  potential,  many  developers  of 
exceptionally  low  potential  giving  much  fog; 

With  most  developers  the  growth  of  fog  is  affected  to  a 
very  much  greater  extent  by  bromide  than  is  the  growth  of 
image  density; 

For  a  developer  of  relatively  high  reduction  potential 
(monomethylparaminophenol,  pyrogallol,  etc.),  an  amount 
of  bromide  sufficient  practically  to  inhibit  fog  even  with 

68 


THE  THEORY  OF  DEVELOPMENT 

relatively  prolonged  development  does  not  greatly  affect  the 
density  (i.  e.,  the  depression  is  small)  provided  the  concentra- 
tion of  the  developing  agent  is  great  enough. 

In  other  words,  for  the  preceding  conditions,  bromide  cuts 
down  the  fog  but  does  not  lower  the  effective  speed  of  the 
plate. 

As  a  general  rule,  therefore  (other  conditions  being  equal), 
there  is  an  advantage  in  the  use  of  a  high  reduction  potential 
developer  of  suitable  character  with  enough  bromide  to 
minimize  chemical  fog. 

In  speed  determinations  on  ordinary  emulsions,  especially 
if  developers  or  emulsions  apt  to  fog  are  used,  it  is  a  distinct 
advantage  to  use  bromide.  If  no  bromide  is  used,  b  is  assumed 
0,  which  is  true  for  nearly  all  ordinary  plates,  a  is  not  affected 
by  bromide.  The  speed  may  therefore  be  determined  with 
sufficient  bromide  to  eliminate  the  fog  error.  (See  Chapter 
VIII  on  distribution  of  fog  over  the  image.) 

3.    EFFECT  OF  THE  DEVELOPING  AGENT 

This  is  another  question  which  has  been  the  subject  of 
much  discussion.  While  the  determination  of  emulsion 
speeds  for  different  ordinary  emulsions  may  be  made  easily, 
the  same  measurements  with  many  different  developing 
agents  on  a  plate  of  sufficient  latitude  (usually  a  moderately 
fast  plate),  will  be  attended  by  many  difficulties.  This  is 
especially  true  for  developers  such  as  those  employed  in  the 
present  work,  where  the  concentrations  are  always  the  same, 
and  no  attempt  is  made  to  obtain  good  practicable  formulae. 
This  series  of  developers  represents  similar  conditions  chem- 
ically, and  we  believe  that  on  the  whole  the  results  are  of 
value  from  the  theoretical  point  of  view.  It  is  emphasized 
here  and  later  that  little  practical  importance  is  attached  to 
the  data  (given  below),  on  the  effect  of  the  developing  agent, 
as  they  would  not  be  duplicated  by  the  use  of  commercial 
developers.  A  similar  application  of  the  method  with  the 
latter,  however,  could  not  fail  to  be  of  value. 

The  greatest  error  in  the  present  problem  is  that  due  to  fog. 
It  has  been  quite  conclusively  demonstrated  that  fog  does  not 
lie  uniformly  distributed  over  the  image,  but  is  greatest  over 
the  low  densities.  Hence  it  is  seen  that  as  fog  increases  it 
can  change  the  character  of  the  plate  curve,  giving  a  false 
result.  This  leads  to  false  values  of  log  i,  of  a,  and  of  b,  or  in 
some  cases  renders  their  determination  impossible  except  over 
the  narrow  range  where  no  fog  is  produced.  In  such  cases 
there  is  great  advantage  in  the  use  of  bromide. 

69 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

In  Table  11  are  given  results,  obtained  with  seven  developers 
used  on  a  Seed  23  emulsion.  These  were  obtained  from 
bromide  depression  data,  so  that  the  value  of  a  is  the  average 
from  determinations  at  several  concentrations  of  bromide, 
and  may  therefore  be  considered  quite  reliable,  b  was 
zero.  The  speed  numbers  (H)  are  found,  as  above,  from 
log  H  =  log  k  —  a  +  b,  where  k  is  100  and  a  is  expressed  in 
units  of  log  E  Relative.  The  reduction  potentials  of  the  de- 
velopers are  recorded  also. 

TABLE  11 

INFLUENCE  OF  THE  DEVELOPING  AGENT  ON  PLATE  SPEED 

(b  =  Q) 

Developer  ^Br  a  H 

M/20  Hydroquinone 1.0  .07  85 

Paraphenylglycine 1.6  .12  76 

Toluhydroquinone 2.2  — .  24  174 

Paraminophenol  hydrochloride 6  .49 

Chlorhydroquinone 7  .10  80 

Bromhydroquinone 21  .49 

Monomethylparaminophenol  sulphate 23  .       .63  23 

There  is  no  regularity  in  these  results.  On  another  and 
faster  emulsion  the  following  were  obtained : 

TABLE  12 

Developer  ^Br               a  H 

Paraphenylglycine 1.6  — .17  148 

Paraminophenol  hydrochloride 6  + .  12  76 

Dimethylparaminophenol  sulphate 10  +  .  28  53 

Pyrogallol 16  -  .05  112 

Again  no  connection  between  reduction  potential  and  plate 
speed  is  apparent.  However,  pyrogallol,  paraminophenol, 
and  dimethylparaminophenol  stand  in  the  same  order  as  to 
speed  as  in  Table  10. 

Table  13  gives  results  less  reliable  than  those  above,  as  the 
data  were  obtained  incidentally  to  other  work  for  which  no 
bromide  was  used.  The  range  of  developing  agents  is  much 
greater  and  the  same  general  trend  is  indicated  as  in  Tables 
11  and  12,  though  the  results  are  somewhat  erratic  and  some  of 
them  no  doubt  are  erroneous.  Each  value  of  a  is  the  result  of 
but  one  determination,  and  that  without  bromide.  The 
D-y  curve  for  each  case  is  based  on  from  ten  to  twenty  pairs 
of  plates,  plates  showing  bad  fog  being  included.  The 
determinations  marked  with  an  X  are  from  the  most  consistent 
data.  A  Seed  30  emulsion  was  used  throughout  and  all  the 
conditions  were  as  previously  described. 

70 


THE  THEORY  OF  DEVELOPMENT 

TABLE  13 

INFLUENCE   OF  THE   DEVELOPING   AGENT   ON   PLATE   SPEED 

Experiment 

Number "^Br          a       b         H 

131  M/10  Ferrous  oxalate 0.3  0       0    X    100 

132  M/20  Paraphenylenediamine  hydrochlor- 
ide,  no  alkali 0.3      -  .52     0         330 

126  M/20  Hydroquinone 1.0      -.66     0X460 

136  M/20  Toluhydroquinone -.24  0  X  175 

123-140  M/20  Paraminophenol  hydrochloride. .  .  6  . 12  0  X  76 

165-167  M/20  Chlorhydroquinone 7 .20  OX  63 

127  M/20  Paramino-orthocresol  sulphate..  .  7  -.54  0  X  350 
125       M/20  Dimethylparaminophenol sulphate  10  -.32  0  X  210 

124       M/20  Pyrogallol 16  -.88  0  X  760 

135       M/20  Monomethylparaminophenol  sul- 

phate 20 0       0   X    100 

144  M/25  Bromhydroquinone 21  T20     0    X     63 

130       M/20  Methylparamino-orthocresol .  .  .  .    23          -  .  78     0         600 

145  M/20  Diamidophenol  hydrochloride,  no 
alkali 30-40        . 20     0  63 

129       M/20  Dichlorhydroquinone -.48     0X300 

133  M/20  Dibromhydroquinone -  .  60     OX   400 

137  M/20  Paraminomethylcresol  hydrochlo- 
ride -1.00     0   X1000 

146  M/20  Diamidophenol,  +  alkali -.60  OX   400 

154  M/20  Pyrocatechin +.26  0    X     55 

172  M/20  Phenylparaminophenol -.06  0X115 

184  M/20  Edinol +.46  0           35 

195  M/20  Eikonogen -.26  0         180 

193  M/20  Hydroxylamine  hydrochloride  + 

q.25M,NaOH +.12     0  76 

194  Commercial  Pyro  Developer  (containing 

bromide) .- +.20     0          .63 

Log  E  =  2.4  (relative  scale) 
Seed  30  Emulsion 

We  doubt  that  such  wide  deviations  occur.  Indeed,  this 
conclusion  is  upheld  by  the  fact  that  if  a  certain  fixed  exposure 
which  gives  densities  lying  well  up  on  the  plate  curves,  out  of 
the  region  of  fog,  is  selected,  the  densities  (on  prolonged 
development,  at  least),  vary  with  the  developer,  showing  a 
general  tendency  to  increase  with  reduction  potential.  But 
the  variation  is  not  so  great  as  these  speed  values  would  indi- 
cate. Consequently  we  must  attribute  some  of  this  deviation 
to  fog,  which,  as  indicated,  can  change  the  contrast  and  inertia 
values. 

It  is  clear  from  the  above  and  from  many  other  experiments 
that  variations  of  emulsion  speed  with  developing  agents  are 
far  from  orderly,  and  that  the  speed  obtained  in  a  given  case 

71 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


depends  on  several  factors,  among  which  are,  undoubtedly, 
the  reduction  potential  of  the  developer,  the  general  balance 
of  the  ingredients  of  the  solution  (which  conditions  hydrolysis 
and  the  character  of  secondary  reactions),  the  physical  action 
of  the  developer  on  the  gelatine  and  on  the  silver  halide,  and 
the  fogging  propensity  of  the  developer.  From  data  on 
velocity  and  maximum  density,  to  be  presented  later,  it  is 
concluded  that,  other  conditions  being  equal,  the  speed 
increases  somewhat  with  increasing  reduction  potential.  At 
any  rate,  it  should  not  be  concluded  that  the  deviations  found 
(especially  those  in  Table  13)  necessarily  obtain  for  any  condi- 
tions other  than  those  described.  It  will  be  found  that  the 
results  with  commercial  developing  formulae  are  much  more 
nearly  balanced. 

4.  INFLUENCE  OF  THE  CONCENTRATIONS  OF  THE 
OTHER  INGREDIENTS  OF  THE  DEVELOPER 

These  complex  effects  are  not  capable  of  ready  interpreta- 
tion. As  the  state  of  balance  among  the  various  ingredients 
of  the  developers  is  changed  the  degree  of  hydrolysis  and 
dissociation  of  the  developing  substance  varies.  The  physical 
action  of  the  developing  solution  probably  changes  to  some 
extent  also.  To  these  and  to  the  other  factors  mentioned 
above  we  may  attribute  the  results,  but  without  definite 
knowledge  that  it  is  correct  to  do  so. 

The  changes  in  the  constant  a  for  the  hydroquinone  devel- 
oper are  shown  in  Fig.  26.  The  concentrations  of  sulphite, 

CHANGES  IN  HYDROQUnUM  DtV  NO  BROMIDE  USED    SE1030 


<u*.~u*     ai3           azs           125           25.            5 

1       75.   100.      ISaZOO.              CONC.INWSA1TCR 

h 

YDROQUINOHE 

A->C03      SO  GM 

ffi 

t\ 

VL 

1 

^-  *• 

^ 

SI 

/ 

1                                                                   WDROQUINOHEi 

3)3     445     625              125              25i                50                  100.             1 

^NAZSQ3SO<MS/L 

f 

^^^ 

"^ 

-^^C 

i 

__^-  —  ^ 

^~-—  — 

—  •       ( 

) 

( 

) 

IS              J 

S        ^ 

F       Jir 

VAzSOs-S 

VGM 
OGM 

Sj( 

S 

! 

. 

/ 

\ 

> 

f 

\ 

/ 

\, 

( 

s 

\ 

>) 

Figs.  26- A,  B  and  C 

72 


THE  THEORY  OF  DEVELOPMENT 

carbonate,  and  hydroquinone  were  varied  as  indicated.  Vari- 
ation in  bromide  concentration  produces  no  change  in  a,  as 
previously  shown. 

The  lower  the  value  of  a  here,  the  higher  the  speed.  In  all 
cases  b  =  0. 

There  is  practically  no  change  in  speed  with  changing 
sulphite  concentration  over  a  wide  range  (Fig.  26A). 

There  is,  however,  a  marked  increase  of  speed  as  the  alkali 
concentration  is  increased  until  a  maximum  is  reached,  after 
which  the  speed  decreases  (a  increases).  (Fig.  26B).  This 
may  be  accounted  for  by  the  hydrolysis  relations  and  also  by 
the  physical  effect  of  the  alkali  on  the  gelatine,  excess  of  alkali 
causing  a  hardening  of  the  gelatine,  while  over  the  lower 
range  a  gradual  softening  takes  place. 

Insufficient  data  were  obtained  on  variations  of  hydro- 
quinone concentration,  but  such  results  as  are  available  are 
shown  in  Fig.  26C. 

It  is  to  be  understood  that  these  relations  may  be  quite 
different  writh  other  developing  agents. 

5.    PRECISION    OF    THE    METHOD.       RESULTS     WITH    COMMERCIAL 
EMULSION  AND  DEVELOPER 

The  data  in  Table  14  illustrate  the  precision  wrhich  can  be 
attained  by  the  use  of  the  method  described  above.  Under 
favorable  conditions  the  original  Hurter  and  Driffield  method 
was  found  to  give  slightly  greater  deviations  from  a  mean. 
Under  less  favorable  conditions  the  Hurter  and  Driffield 
method  would  require  modification  to  approach  the  reproduci- 
bility  and  consistency  of  the  method  described  here. 

A  panchromatic  plate  was  used  with  a  commercial  pyrogallol 
developer.  Exposures  were  made  under  varying  conditions 
which  need  not  be  described  at  present.  Five  pairs  of  plates 
were  used  for  each  determination  of  a.  Three  separate  deter- 
minations were  made,  numbered  1,  2,  and  3.  AS  is  the 
deviation  from  average  speed. 


TABLE  14 

I 

II 

III 

IV 

Speed 

1     85.0 
2     77.5 
3     79.3 

A5 
+4.8 
-2.7 
-1.9 

Speed 
66.0 
59.2 
68.2 

A5 
+  1.5 
-5.2 

+3.7 

Speed 
54.0 
52.8 
57.9 

AS 
-0.9 
-2.1 
+3.0 

Speed 
33.9 
31.7 
38.9 

A5 
-0.9 
-3.1 
+4.1 

Mean  80.2 
Average 
deviation 

2 

.8% 

64.5 

5.4% 

54 

.9 

36% 

31 

8 

7.8% 

73 

MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

The  deviations  for  sixteen  such  cases  averaged  2.3  per  cent. 
The  old  (H.  and  D.)  method  carried  out  in  exactly  the  same 
way  for  sixteen  cases  gave  3.3  per  cent  deviation.  For  the 
latter  the  inertia  points  of  five  pairs  of  plates  were  averaged. 
In  the  usual  routine  application  of  this  method  but  two  pairs 
are  used. 

CONCLUSIONS 

The  inertia  point  is  not  a  fixed  characteristic  of  an  emulsion, 
and  it  is  better  to  avoid  the  use  of  i  or  log  i  as  constants 
wherever  possible. 

More  fundamental  sensitometric  constants  for  given  condi- 
tions are  a  and  b,  the  coordinates  of  the  point  of  intersection 
of  the  H.  and  D.  straight  lines  obtained  by  varying  the  times 
of  development. 

a  and  b  are  determined  from  the  relations 

a   =  log  E  —  6 
b   =    -A6 

by  the  use  of  the  Z>-y  function,  for  which  6  is  the  slope 
and  A  the  intercept  on  the  y  axis.  Log  E  is  the  standard 
exposure  for  which  the  D-f  curve  is  plotted. 

When  b  =  0  the  H.  and  D.  straight  lines  intersect  on  the 
log  E  axis.  This  is  true  for  nearly  all  ordinary  emulsions  and 
for  developers  containing  no  bromide. 

If  sufficient  bromide  is  present  b  differs  from  zero  and 
increases  (negatively)  with  increasing  bromide  concentration. 
In  such  cases  the  new  method  is  of  advantage  in  interpreting 
the  results. 

A  few  of  the  slower  emulsions  contain  free  bromide,  so  that 
they  exhibit  a  regression  of  inertia  with  increasing  develop- 
ment— i.  e.,  have  a  non-vanishing  b.  This  effect  is  less  for  an 
emulsion  of  this  kind  when  a  developer  of  high  reduction 
potential  is  used  than  with  one  of  low  reduction  potential. 

If  bromide  is  present  in  the  developer,  the  relations  are  the 
same  as  in  the  preceding.  A  developer  of  high  reduction 
potential  may  be  used  with  more  bromide  without  lowering 
the  effective  speed. 

There  is  considerable  advantage  in  the  use  of  a  suitable 
developer  of  high  reduction  potential  with  enough  bromide 
to  cut  down  fog. 

In  many  cases,  speed  determinations  are  made  more  easily 
if  bromide  is  used  judiciously. 

74 


THE  THEORY  OF  DEVELOPMENT 

The  emulsion  speed  does  not  vary  consistently  with  any 
known  characteristic  of  a  developer,  but  is  probably  affected 
by  the  factors  noted  above.  Others  of  these  factors  being 
the  same,  it  is  believed  that  the  speed  increases  with  increasing 
reduction  potential. 

The  method  of  speed  determination  described  can  be  made 
sufficiently  accurate  for  all  ordinary  emulsions  and  developers. 

The  conclusions  reached  apply  only  to  the  conditions  stated 
— i.  e.,  for  the  region  of  correct  exposure  (the  straight  line 
portion  of  the  plate  curve) — just  as  in  the  original  speed 
determinations  by  Hurter  and  Driffield.  A  separate  investiga- 
tion will  be  required  to  measure  relative  speeds  for  the  region 
of  under-exposure.  However,  so  far  as  the  effect  of  the 
developer  is  concerned  (as  studied  here),  the  relations  would 
not  be  different. 


75 


CHAPTER  V 

Velocity  of  Development,  the  Velocity  Equation, 

and  Methods  of  Evaluating  the  Velocity 

and  Equilibrium  Constants 

In  preceding  chapters  an  attempt  has  been  made  to  study 
the  affinities  of  certain  organic  reducing  agents,  and  to  correlate 
their  photographic  properties  on  this  basis.  However  careful 
such  work  may  be  it  cannot  be  entirely  successful  because  the 
reduction  potential  of  a  developer  is  not  always  the  chief 
property  in  conditioning  the  nature  of  its  photographic 
action.  Moreover,  other  properties  important  in  this  respect 
are  relatively  unknown,  which  makes  a  fair  quantitative 
comparison  of  developing  agents  extremely  difficult.  Among 
factors  influencing  the  results  of  such  comparisons  we  may 
mention  those  contributing  to  differences  in  reaction  resist- 
ance, in  physical  action  (adsorption,  penetration,  effect  of 
tanning,  etc.),  and  in  the  chemical  system  affecting  the  entire 
reaction.  The  reaction  resistance  is  influenced  by  factors  of 
which  we  know  little.  The  solvent  action  of  the  developer 
on  silver  bromide,  the  nature  of  the  chemical  reactions  among 
the  ingredients  of  the  solution  (developing  agent,  alkali,  and 
sulphite),  the  degrees  of  dissociation  and  hydrolysis  of  the 
resultant  compounds,  and  the  effects  of  relatively  high  concen- 
trations of  other  ions — all  these  influence  reaction  resistance 
and  determine  the  chemical  state  of  the  system. 

It  was  felt  that  a  study  of  reaction  velocities  might  lead 
to  a  better  understanding  of  these  questions,  and  the  work 
about  to  be  described  was  undertaken. 

In  working  out  methods  for  the  study  of  the  velocity  of 
development,  it  was  decided  not  to  make  use  of  the  relation 
between  the  contrast  (gamma)  of  the  plate  and  the  time  of 
development,  as  has  been  done  to  some  extent  by  other 
investigators,  but  to  use  the  chemically  more  logical  quantity 
density  (D),  which  has  been  defined  as  being  proportional  to 
the  mass  of  silver.  The  problem  thus  becomes  a  physico- 
chemical  one,  dealing  with  familiar  relations  and  quantities. 
It  is  evident  that  here  we  are  dealing  with  a  heterogeneous 
reaction  very  probably  susceptible  to  disturbing  influences, 
as  such  reactions  often  are.  A  rough  preliminary  analysis  of 
one  case  will  show  the  method  of  examining  the  velocity  and 

76 


THE  THEORY  OF  DEVELOPMENT 

acceleration  curves.  The  data  were  obtained  by  developing 
a  pure  silver  bromide  emulsion  in  M/20  paraphenylglycine 
(with  50  grams  of  sulphite  and  50  grams  of  carbonate  per  liter) 
which  contained  M/100  potassium  bromide.  In  Fig.  27A 
density  (D)  is  plotted  against  the  time  of  development  for  a 
fixed  exposure,  as  will  be  explained  directly.  The  slope  of  the 
curve  at  any  time  (t)  is  the  velocity  of  development  at  that 
instant.  By  plotting  the  velocity  against  the  time  the 
so-called  acceleration  curve,  Fig.  27B,  is  obtained.  The 
velocity  is  expressed  in  terms  of  density  developed  per  minute. 


a^ 

s*^~~ 

^_ 

5  min.  T       10           15            20 

Fig.  27-A 

Velocity 
of  Dev. 


A, 

/\ 

I 

^ 

>  —  •  __ 

5  min.  T              10                  1 
Fig.  27-B 

The  example  chosen  shows  a  well  defined  period  of  induction, 
or  period  of  increasing  velocity — a  characteristic  of  photo- 
graphic development,  but  not  always  so  well  shown.  In 
fact,  in  many  cases  it  is  practically  absent,  and  unless  the 
experimental  work  is  exceptionally  accurate  it  is  best  ignored. 
However,  the  existence  of  this  period  of  induction  has  been 
generally  recognized  as  a  feature  of  the  kind  of  reaction  we 
are  investigating  here.  It  is  evident  from  the  figures  that 
more  or  less  time  elapses  before,  there  is  measurable  develop- 
ment, and  that  the  velocity  then  rapidly  rises  to  a  maximum, 
after  which  it  decreases  in  the  usual  way  as  the  amount  of 
material  remaining  to  be  acted  upon  decreases. 

A  period  of  acceleration  or  induction  is  usually  accounted 
for  by  inherent  reaction  resistance  or  by  the  reaction  taking 
place  in  a  series  of  intermediate  steps,  or  by  both.  The 
factors  generally  considered  important  in  producing  a  period 
of  induction  in  photographic  development  are  (1)  the  time 
required  for  the  invasion  of  the  developer,  and  (2)  the  time 
required  to  saturate  the  solution  in  the  emulsion  with  silver 
after  reduction  begins.  Neither  seems  to  the  writer  to 
account  sufficiently  well  for  the  long  periods  of  delay  observed 
with  some  developers.1 

1  See  Sheppard,    S.  E.  and  Meyer  G.,    Chemical  induction  in  photographic  develop- 
ment.    J.  Amer.  Chem.  Soc.  42  :  689.  1920. 

77 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

It  should  be  understood  that  the  period  of  acceleration, 
or  what  is  termed  the  period  of  induction,  is  ignored  in  the 
present  discussion,  as  it  is  generally  of  short  duration.  The 
term  refers  to  the  delay  before  the  reaction  begins. 

It  may  be  seen  from  a  first  analysis  that  velocity  curves 
of  the  usual  kind  are  obtained,  and  that  these  should  be 
capable  of  interpretation  by  ordinary  methods.  The  imme- 
diate problem,  therefore,  is  to  investigate  the  possibility  of 
fitting  a  mathematical  expression  to  the  experimental  data  on 
velocity  of  development — that  is,  an  equation  which  properly 
describes  the  course  of  reaction  with  time.  Having  found 
methods  for  doing  this,  it  becomes  possible  to  compare  devel- 
opers and  to  discover  what  effect  various  conditions  have  on 
both  the  velocity  and  the  end-point. 


PREVIOUS  WORK  ON  VELOCITY  EQUATIONS 

Hurter  and  Driffield  first  formulated  the  relation  between 
the  density  produced  for  a  given  exposure  and  the  time  for 
which  the  plate  had  been  developed,  using  the  expression 

D   --  Dm  (l-flt)f  (17) 

where  D  is  the  density  at  time  /,  D  oo  the  ultimate  density,  and 
a  a  constant.  This  equation  was  based  on  certain  assumptions 
as  to  the  arrangement  of  the  silver  bromide  particles  affected 
by  light  and  as  to  the  mechanism  of  penetration  and  reduction 
by  the  developer.  These  assumptions  were  later  questioned 
and  are  now  practically  discredited. 

However,  Sheppard  developed  in  a  different  way  an  equa- 
tion resembling  that  of  Hurter  and  Driffield.  He  found  that 
the  velocity  of  development  was  obtainable  by  the  expression 

^    =  K(Dm  -  D),  (18) 

where  as  usual  D  signifies  the  density  at  time  /,  D  oo  the  ulti- 
mate density,  a  quantity  proportional  to  the  mass  of  latent 
image,  and  K  a  constant.  Sheppard  deduces  that  K  is  equal  to 

-~-,  A  being  the  diffusion  constant  for  the  developer,  a  the 
o 

concentration  of  the  developer,  and  5  the  "diffusion  path." 
This  simple  expression  (equation  18)  for  a  heterogeneous 
reaction  is  obtained  by  assuming  that  the  velocity  of  develop- 
ment depends  chiefly  on  diffusion  processes.  There  is  much 
experimental  evidence  to  support  this  view.  Nernst  developed 
a  theory  for  reaction  velocities  in  heterogeneous  systems, 

78 


THE  THEORY  OF  DEVELOPMENT 

assuming  that  diffusion  is  predominant.  But  this  theory 
evidently  does  not  take  into  account  all  the  phenomena 
encountered. 

Basing  his  reasoning  on  Wilderman's  theory,  Sheppard 
formulates  for  the  case  of  ferrous  oxalate  a  more  complete 
expression  for  the  velocity,  which  includes  the  view  that 
development  is  a  reversible  reaction.  Omitting  the  inter- 
mediate steps  we  may  write  this  equation 


Here,  a,  b,  h,  and  d  are  constants  which  include  such  factors 
as  equilibrium  constants  for  the  various  reactions  considered, 
equilibrium  concentrations,  and  surfaces  of  the  developable 
halide  and  of  silver. 

By  replacing  b  and  a  in  such  a  way  that  b/a  =  pg,  where 
f  represents  the  equilibrium  constant  of  development,  the 
above  equation  becomes,  on  integration  (as  suggested  by 
Colby), 


Kl  -  log  -  "* 


Upon  closer  examination,  this  relation  is  seen  to  resemble 
the  integrated  form  of  equation  18,  which  is 


Kt  ' 


In  equation  20,  p  f  represents  the  equilibrium  value  of  the 
density  developed,  or  the  maximum  density  corresponding  to 
#00  in  (21).  Z>ooas  used  in  (20)  indicates  the  density  or  mass 
of  latent  image  which  can  be  developed  in  the  given  case  on 
infinite  development,  p  %  therefore  tends  to  approach  D  <&  , 
depending  on  a  number  of  conditions  which  will  be  enumerated 
elsewhere.  Equation  20  differs  from  (21)  in  that  there  is  a 
correction  term  in  the  former  which,  as  Sheppard  states, 
expresses  the  effect  of  reversibility,  but  is  of  importance 
only  when  there  is  a  high  concentration  of  bromide  or  of  the 
oxidized  developer. 

In  ordinary  alkaline  development  there  are  disturbing 
factors  which  are  not  included  in  equation  20,  so  that  this  is 
probably  only  an  approximation.  In  fact,  it  has  been 
obtained  by  a  rather  free  use  of  assumptions  as  to  the  state  of 
balance  among  the  various  reactions.  Other  reactions  which 
disturb  this  balance  may  occur.  Even  if  we  could  determine 

79 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


these  disturbing  influences  and  their  effect  the  velocity  func- 
tion would  probably  be  so  complicated  that  it  could  not  be 
integrated  to  any  useful  form.  Because  of  the  very  great 
difficulties  of  enumerating  the  constants  p,  %,  d,  and  h, 
especially  in  alkaline  development,  and  because  of  our  present 
lack  of  knowledge  of  the  mass  of  the  latent  image,  it  is  impos- 
sible to  test  this  equation.  This  matter  will  be  discussed 
more  fully  after  more  experimental  evidence  has  been 
presented. 

EXPERIMENTAL  METHODS 

The  general  methods  used  by  Hurter  and  Driffield  and  by 
Sheppard  and  Mees  were  followed  in  the  present  work,  with 
such  modifications  as  seemed  necessary.  Although  in  general 
the  entire  procedure  resembles  very  closely  that  used  in  other 
chemical  kinetic  investigations,  the  reader  who  has  but 
little  occasion  to  interpret  sensitometric  data  may  find  it 
somewhat  confusing.  For  this  reason  the  methods  will  be 
described  in  some  detail. 

It  is  our  purpose,  first,  to  construct  for  a  given  constant 
exposure  a  curve  showing  the  growth  of  density  with  time  of 
development.  Since  (under  usual  conditions),  density  is 
proportional  to  mass  of  silver,  there  results  a  velocity  curve 
of  the  usual  type,  showing  the  amount  of  silver  produced  at 
any  time  of  development  /.  To  obtain  this  it  is  sufficient 
to  illuminate  a  plate  uniformly,  cut  it  up  into  strips,  and 
develop  the  strips  under  constant  conditions  for  different 
lengths  of  time.  After  fixing,  washing,  and  drying,  the 
densities  of  the  various  strips  may  be  determined  and  plotted 
against  the  time  of  development  corresponding  to  each 
density.  But  lack  of  sufficient  uniformity  in  exposure  and 
in  sensitiveness  of  large  plates,  as  well  as  a  rather  high  per- 
centage of  accidental  errors,  make  this  procedure  less  reliable 
than  is  required  in  the  present  investigation. 

Better  results  are  obtained 
from  the  type  of  data  menti- 
oned in  previous  chapters,  and 
much  of  the  same  material  can 
be  used  here.  It  has  been 
shown  that  a  series  of  plates, 
exposed  in  the  sensitometer 
in  a  definite  way,  and  devel- 
oped for  varying  times,  gives 
a  series  of  H.  and  D.  curves 
Fig  28  the  straight  line  portions  of 

80 


THE  THEORY  OF  DEVELOPMENT 

which  meet  in  a  point  (for  practically  all  cases  where  emul- 
sion or  developer  do  not  contain  soluble  bromides).  Fig.  28 
shows  this  for  the  normal  unbromided  developer. 

The  toe  and  shoulder  of  the  H.  and  D.  curve  are  drawn 
for  the  upper  and  lower  curves  only.  The  lines  represent  the 
straight  line  portions  of  the  H.  and  D.  curves  for  plates 
developed  for  the  times  fa,  etc.,  up  to  too  •  Similar  data  were 
obtained  in  the  study  of  reduction  potential  by  exposing  plates 
in  a  sensitometer  and  developing  them  in  pairs  for  varying 
times  at  a  constant  temperature  in  a  thermostat,  as  previously 
described. 

If,  now,  we  take  a  cross  section  of  this  series  of  curves  at 
AB — i.  e.,  use  a  standard  value  of  log  E,  we  have  the  informa- 
tion desired — the  growth  of  density  with  time  of  development, 
the  exposure  being  fixed.  This  method  is  somewhat  more 
accurate  than  that  of  using  a  single  flashed  plate,  as  first 
described,  because  if  we  use  the  value  Z)6,  for  example,  as  the 
intersection  of  the  H.  and  D.  smoothed  curve,  and  AB,  its 
value  is  influenced  by  the  values  obtained  for  the  other  densi- 
ties on  the  plate.  That  is,  DG  represents  an  average  of  several 
values.  Any  one  attempting  sensitometric  work  on  a  large 
scale  will  appreciate  some  of  the  difficulties  encountered  as 
well  as  the  desirability  of  these  methods. 

As  stated  above,  it  has  been  found  that  with  many  of  the 
developers  used  commercially  and  with  good  plates  and  care, 
uniform  and  consistent  results  may  be  obtained.  But  when  a 
large  number  of  different  developers  in  which  the  equivalent 
concentrations  of  all  the  ingredients  are  always  the  same  are 
used  on  a  large  number  of  different  emulsions,  many  and  wide 
variations  are  likely  to  occur,  probably  because  some  of  the 
developers  so  made  are  not  practically  useful.  But  for 
purposes  of  comparison  it  is  important  to  use  developing 
agents  at  the  same  equivalent  concentration,  and  this  almost 
no  previous  workers  (except  Sheppard  and  Mees)  have  done. 

Returning  to  the  discussion 
of  the  curves,  the  value  for  the 
density  coordinates  of  the  inter- 
sections of  AB  with  the  straight 
lines  plotted  against  the  cor- 
responding times  of  develop- 
ment give  a  curve  similar  to 
that  shown  in  Fig.  29,  in 

which  the  period  of  induction 

T  •«•.»«>  is    disregarded,     as    explained 

Fig.  29  above.     The    curve,    which    is 

81 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

at  least  roughly  exponential,  has  coordinates  in  terms  of  mass 
of  silver  and  time  of  development. 

Experimental  evidence  of  this  kind  has  made  it  possible  to 
study  the  properties  of  the  curves,  thereby  explaining  some 
of  the  relations  between  the  photographic  and  the  chemical 
properties  of  the  developing  agents  used.  In  studying  the 
velocity  curves  about  15,000  plates,  exposed  to  acetylene 
screened  to  daylight  quality  in  a  sliding-plate  (non- 
intermittent)  electrically  operated  sensitometer,  and  developed 
in  various  water- jacketed  tubes  and  tanks  supplied  by  water 
at  20°  C.  from  a  thermostat,  were  examined.  A  constant 
value  of  the  exposure  was  used  in  plotting  the  data.  This 
exposure  (log  E  =  2.4)  represented  1.4  candle  meter-seconds 
of  screened  acetylene. 

As  stated  in  a  previous  chapter,  all  developers  were  made 
up  to  standard  concentration  and,  unless  otherwise  specified, 
every  developer  contains  in  one  liter  1/20  of  the  gram- 
molecular  weight  of  the  developing  agent  with  50  grams  per 
liter  each  of  sodium  sulphite  and  sodium  carbonate.  No 
bromide  or  other  substances  are  present  unless  so  stated. 

A  number  of  different  emulsions  and  developing  agents  were 
examined,  of  which  a  few  will  be  described.  It  is  obviously 
impossible  to  record  the  results  of  many  of  the  experiments. 

INTERPRETATION  OF  RESULTS 

Taking  up  first  an  analysis  of  the  curves,  the  experimental 
results  of  previous  workers  as  well  as  theoretical  deduction 
have  indicated  that  the  relation  between  density  and  time  of 
development  at  constant  exposure  may  be  expressed  by  an 
equation  of  the  general  type 

Kt   =  log  nDc°  n  or    D   =  D«>  (l-*-*0.  (22) 

Lf  co  — D 

This  form  would  indicate  that  photographic  development 
proceeds  approximately  in  accordance  with  the  law  for  a 
unimolecular  homogeneous  reaction,  and  that  the  concentra- 
tion of  only  one  substance,  the  silver  halide  forming  the  latent 
image,  is  changing.  Hurter  and  Driffield  gave  very  meager 
data  in  support  of  their  equation.  The  results  obtained  by 
Sheppard  and  by  Sheppard  and  Mees,  who  investigated  the 
relation  much  more  thoroughly,  especially  for  ferrous  salts, 
indicate  that  the  ferrous  salts  as  developers  (acid  developers) 
follow  this  law  rather  closely.  The  results  obtained  with 
alkaline  developers  did  not  fit  the  equation  so  well,  though 
the  range  of  times  used  was  too  small  for  conclusive  evidence. 

82 


THE  THEORY  OF  DEVELOPMENT 

The  writer,  working  over  a  much  greater  territory,  finds  many 
cases  where  the  expression  under  consideration  does  not  fit  the 
results  at  all.  The  general  conclusions  reached,  however,  are 
capable  of  interpretation  in  harmony  with  Sheppard  and 
Mees'  results. 

It  is  hardly  to  be  expected  that  the  course  of  so  complicated 
a  process  as  photographic  development  in  the  presence  of 
alkali  could  be  described  by  so  simple  a  law,  since  we  know  of 
changes  which  take  place  at  various  stages.  Even  if  the  law 
formulated  in  equation  22  held  approximately  over  a  consid- 
erable range,  there  are  possibilities  of  several  complications 
which  might  increase  in  importance  as  time  went  on,  or  be  of 
more  importance  in  the  early  stages  of  the  process,  thereby 
giving  rise  to  departures  from  this  law.  For  example,  it  is 
unlikely  that  diffusion  of  the  developer  into  the  gelatine  emul- 
sion and  of  the  reaction  products  out  of  it  is  the  simple  process 
assumed.  Through  absorption  and  various  other  physical 
phenomena,  relatively  large  local  changes  in  the  concentration 
of  the  developer  may  occur.  In  such  a  case,  development 
might  approximate  a  second  order  reaction,  the  velocity  being 
proportional  both  to  the  mass  of  latent  image  remaining  to  be 
reduced  and  to  the  concentration  of  the  developer.  That  is, 
the  quasi-bimolecular  form, 

42   =  K(Dm-  D)   (A  -  D),  (23) 

may  be  a  more  nearly  correct  expression.  A  is  the  concen- 
tration of  the  developer  at  the  beginning  and  D  equivalents 
have  been  used  at  the  time  t.  The  integrated  form  of  (23)  is 

K     =    log    7= zrr ~. 


If  over  a  range  of  times  D  is  small  compared  with  A  (and 
this  is  often  the  case,  a  very  small  amount  of  silver  being 
formed  compared  with  the  amount  of  developing  agent 

A    —  D 

present),  then is  nearly  equal  to  unity,  and  equation  24 

A 

becomes  practically  the  first  order  form.  But  if  because  of 
the  tanning  of  gelatine,  or  by  other  mechanical  means,  inclu- 
sion of  the  developer  occurs,  so  that  its  local  concentration 
changes  as  time  goes  on,  then  a  gradual  departure  from  the 
first  order  law  takes  place.  Something  like  this  does  occur, 
but  the  phenomena  are  undoubtedly  more  complex  than  the 
above  explanation  suggests. 

83 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

It  is  not  impossible  that  two  successive  reactions  of  the 
first  order  take  place,  giving  rise  to  disturbing  influences  at 
the  beginning.  As  Mellor  points  out,  if  ki  and  &2  for  two 
such  reactions  are  widely  different,  the  general  trend  of  the 
reaction  is  a  close  approximation  to  a  single  first  order  reaction 
after  "initial  disturbances,"  and  the  sooner  they  take  place 
the  greater  the  ratio  ki/kz. 

It  is  not  intended  to  advocate  the  view  that  photographic 
development  proceeds  through  a  well  defined  intermediate 
stage,  but  it  has  become  evident  that  many  complex 
phenomena  are  involved  in  the  failure  of  the  reaction  to  follow 
any  definite  law  throughout  its  course,  and  so  little  is  known 
of  the  mechanism  of  the  oxidation  of  the  reducing  agents 
themselves  that  an  intermediate  reaction  is  a  possibility. 

Whatever  views  may  be  held  on  the  matter,  the  best  previous 
work  indicates  that  as  a  first  approximation  the  velocity  of 
development  is  expressed  by  the  ordinary  law  of  mass  action 
for  a  first  order  reaction  as  given  above — 

^     =  K  (Dm  -  D)  or,  integrated,  Kt  =  log  ^"  ^   (21) 

Equation  21  may  be  applied  to  the  density- time  data  as  a 
beginning.  From  it  or  its  exponential  form  D  =  Dm  (1  -  e~~Kt), 
it  is  evident  that  when  /  =  0,  D  =  0;  and  thus  this  equation 
represents  a  family  of  exponential  curves  through  the  origin. 
The  density-time  curve  shown  in  Fig.  29  is  certainly  not  well 
fitted  by  this  form  if  the  curve  intersects  the  horizontal  axis 
very  far  from  the  origin — that  is,  if  the  time  of  appearance  is 
long.  The  method  of  applying  equation  21  to  the  data  is  as 

follows :    If  the  correct  value  of  D  m  is  inserted  and  log  =—    ^-= 

D  oo  —  JD 

plotted  against  the  times  corresponding  to  the  observed  values 

of  D  used  in  log-=—  ^-=  ,  a  straight  line  of  slope  K  is  obtained. 

D  oo      D 

Since  it  is  necessary,  as  shown  above,  that  D  =  0  when  t  =  0, 
it  is  also  a  condition  for  this  graphical  solution  that  the  origin 
be  used  as  a  point  on  the  line — i.  e.,  that  the  straight  line  pass 

through  the  origin.  When  /  =  0  and  D  =  0,  log  -= —  ^-~ 
also  =  0.  The  equation  D  =  D  ^  (1  -  e~Kt)  will  fit  the 

observed  data  over  the  range  of  times  where  log  — —    — ^: 

D  co        Lf 

plotted  against  t  gives  a  straight  line.  Bloch  used  this  method 
incidentally  to  other  work,  but  not  enough  data  are  given  in 

84 


THE  THEORY  OF  DEVELOPMENT 

his  account  to  throw  light  on  the  velocity  equation.  In  the 
present  application  D  oo  is  enumerated  by  trial  and  error,  that 
value  being  taken  which  gives  a  straight  line  over  the  maximum 
range.  However,  in  instances  where  equation  21  fits  at  all 
over  any  range,  the  value  of  D  &>  can  be  approximated  from 
the  experimental  results,  or  may  even  be  obtained  by  long 
development.  The  method  of  choosing  the  value  of  Dm  to 
be  used  and  its  experimental  verification  will  be  given  in 
greater  detail  later. 

It  should  be  noted  that  logarithms  to  the  base  e  are  used 
unless  otherwise  indicated. 

It  was  found  that  equation  21  fitted  the  data  for  only 
those  cases  where  the  time  of  appearance  was  exceedingly 
short,  and  then  only  for  the  early  stages,  usually  for  not  more 
than  three  or  at  the  most  five  minutes'  development.  Many 
cases  could  be  presented  but  space  does  not  permit.  All  the 
experiments  show  that  the  development  reaction  follows  the 
usual  first  order  law  for  a  time  but  that,  on  the  whole,  the 
latter  law  does  not  completely  describe  the  process.  This 
fact,  observed  repeatedly,  makes  it  appear  probable  that  new 
phenomena  predominate  as  development  proceeds. 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


Fig.  30-C 


_0-  —  v 

___  * 

-      —  —  —      < 

f 

1 

T 
Fig.  30-D 

D 


In  Fig.  30  A,  B,  C,  and  D  the 
experimental  results  and  the  den- 
sities computed  from  the  equa- 
tion D  =  Dm  (1  -  e—  Kt)  are 
given .  For  experiments  A ,  B ,  and 
C  an  ordinary  fast  emulsion  was 
used.  iThe  developers  used  were : 


A.  M/20  Paraminophenol  hydrochloride  (pure); 

B.  M/20  Pyrogallol  (pure); 

C.  Same  as  a  +  0.16  M  potassium  bromide; 

D.  M/20  Monomethylparaminophenol  sulphate  of  high  purity. 

Experiment  D  was  carried  out  on  a  slow  emulsion. 

The  constants  to  be  used  in  computing  the  densities  were 
determined  by  the  method  described.  The  attempt  was  made 
in  each  case  to  fit  the  data  over  the  maximum  range  from  the 
beginning.  A,  B,  and  D  are  cases  where  the  time  of  appearance 
is  very  short  and  the  equation  might  be  expected  to  apply. 
With  each  a  value  of  D  m  is  necessary  (in  order  to  give 

1°&  ~ri — °°    n  against  /  as  a  straight  line  through  the   origin) 
D  co  —  L) 

which  is  exceeded  on  longer  development,  as  may  be  clearly 
seen  from  the  figures.  Fig.  30C  is  a  case  in  which  we  could 
not  expect  the  equation  to  apply.  The  time  of  appearance  is 
very  long.  Therefore,  the  computed  and  experimental  curves 
do  not  agree  at  the  beginning,  since  the  equation  necessitates 
a  curve  through  the  origin,  although  no  density  is  obtained 
for  three  or  four  minutes'  development.  For  longer  times 
insufficient  data  were  secured,  so  that  the  usual  departure  in 
the  later  stages  of  development  is  not  evident. 

Fig.  SOD  shows  more  markedly  what  was  often  found  to  be 
the  case — that  the  equation  under  discussion  fits  the  data 
at  the  beginning  and  usually  can  not  be  applied  at  any  other 

86 


THE  THEORY  OF  DEVELOPMENT 


stage  of  the  reaction.  The  method  of  evaluating  the  constants 
for  this  experiment  will  be  given  later,  and  then  the  limited 
application  of  the  simple  first  order  equation  will  be  evident. 
In  this  case  neither  a  higher  nor  a  lower  value  of  D  m  gives 
better  agreement. 

In  case  the  time  of  appearance  is  long — i.  e.,  there  is  a 
considerable  delay — the  velocity  equation  can  be  corrected 
to  a  certain  extent  by  allowing  for  the  initial  period  of  apparent 
inactivity.  In  equation  21  the  correction  is: 


K(t   - 


log 


D 


(25) 


D  co  —  D' 

where    t0   is   the   induction   period.     In   its  exponential   form 
(25)  becomes  D   =  D m    (1     -  e    -«(«-*»)  ).  (26) 

The  velocity  of  the  reaction  is  the  same  as  before,  i.  e., 


dD  v 

—       =  K 


n\ 
-  D). 


Equation  25  is  the  basis  for  applying  the  data.      Log 


D 


is  plotted  against  the  time  as  before,  such  a  value  of  D  m  being 
chosen  as  will  give  a  straight  line  when  observed  values  of 
density  are  inserted,  and  the  function  is  plotted  against  the 
corresponding  times.  The  slope  of  the  straight  line  is  K 
and  the  intercept  on  the  time  axis  gives  /0,  or  the  induction 
period.  K  is  defined  here  in  the  usual  sense,  as  the  velocity 
wrhen  unit  density  remains  to  be  developed. 

This  equation  is  quite  applicable,  however  great  the  period 
of  induction,  but  very  often  the  curves  are  fitted  for  the 
beginning  of  the  reaction  only. 

The  curve  in  Fig.  31  illustrates  the  use  of  equation  26  on 
the  data  used  with  equation  21  in  Fig.  30,  curve  C.  The 
densities  indicated  by  the  circles  are  computed  from  equation 
26,  and  agree  well  with  results  obtained. 

Many  results  were  computed 
for  this  equation.  The  general 
results  tend  to  show  that  the 
corrected  equation  represents 
the  facts  over  a  considerable 
range  from  the  beginning  of  the 
reaction.  The  time  range  for 
which  it  fits  varies  widely,  in 


p. 


some  cases  being  for  only  a  minute,  while  for  others  an  ob- 
served range  of  fifteen  minutes  is  satisfactorily  fitted.     From 

87 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

results  which  will  be  discussed  later  it  is  concluded  that  photo- 
graphic development  represents  .a  series  of  phenomena  which 
change  with  time;  that  because  of  this  fact  it  is  impossible 
or  at  best  very  difficult  to  describe  the  entire  process  by  one 
mathematical  expression;  and  that,  since  the  principal 
information  desired  is  the  value  of  D  m  (the  equilibrium  point 
for  given  conditions),  it  is  justifiable  and  of  more  value  to 
turn  our  attention  to  better  means  of  determining  this  import- 
ant constant,  and  accordingly  to  neglect  the  early  stages  of 
the  reaction. 

The  use  of  equation  25  often  necessitates  values  of  D  ^ 
which  are  obtained  in  a  short  time  and  which  are  greatly 
exceeded  on  longer  development.  Experiments  show  that 
in  the  average  case  the  density  continues  to  increase  for  a 
long  time,  and  that  the  ultimate  density  is  very  likely  to  have 
a  higher  value  than  any  reached  within  the  usual  limits. 

It  was  found  in  the  great  majority  of  cases  that  with  a  fairly 

reasonable  estimate  of  Z)oo  in  the  function   log  =—    °°      the 

D  oo      D 

latter  would  give  a  straight  line  over  a  considerable  range 
when  plotted  against  the  logarithm  of  the  time  instead  of 
against  the  time  itself.  It  was  evident  that  this  method 
would  be  quite  satisfactory  as  giving  an  empirical  expression 
describing  the  reaction  beyond  the  initial  period,  as  the  data 
were  usually  well  fitted  beyond  two  or  three  minutes'  develop- 
ment. In  other  words,  here  the  discrepancies  between  obser- 
vation and  theory  were  at  the  beginning.  This  fact  was  very 
carefully  examined  in  many  cases,  but  in  none  of  them  could 
the  early  stage  be  represented  by  the  expression  used  for  the 
curve  as  a  whole. 

When  log  =; — ^-fpis  plotted  against  log  /  as  just  described, 

D  co       is 

the  equation  for  the  straight  line  is 

K  (log  t  -  log <„)  =  log        Dco     ,  (27) 

LJ  co   —  Lf 

the  slope  being  K  as  before,  and  the  intercept  on  the  log  t 
axis  log  t0.  In  the  exponential  form  this  is 

D  =  Da*  (1    -  «-Kiog<A>)f  (28) 

which,  differentiated  for  the  velocity,  becomes 

JT-T  <*--*>•  (29) 

88 


THE  THEORY  OF  DEVELOPMENT 


So  far  as  the  writer  is  aware  this  is  different  from  other 
*  'corrected"  forms  for  the  velocity  equation,  many  of  which 
have  been  published.  Equation  29  indicates  that  the  velocity 
is  inversely  proportional  to  the  time,  a  fact  for  which  there  is 
no  satisfactory  explanation  at  present.  There  may  be  some 
poisoning  influence  from  oxidation  products  or  the  like,  but 
experimental  evidence  for  this  is  lacking.  It  seems  possible 
that  the  velocity  equation  describes  a  complex  effect  from 
stored  up  oxidation  products,  tanning,  and,  in  general, 
defective  diffusion.  Quantitatively,  this  effect  is  probably 
not  the  simple  function  of  time  required  by  the  above  relation, 
but  the  various  factors  are  taken  up  in  such  a  way  that  K/t 
gives  a  close  approximation  over  a  considerable  range.  Here 
K  is  a  constant,  as  before,  but  its  significance  must  be  different 
since  it  undoubtedly  contains  new  factors.  From  equation 
29,  K  may  be  defined  as  the  product  of  the  velocity  and  the 
time  of  development  when  unit  density  remains  to  be 
developed. 

Fig.  32  illustrates  quite  com- 
pletely the  entire  process  of 
fitting  an  equation  to  the 
data.  The  experiment  was 

«*-  carried  out  with  M  /20  monome- 

f  thylparaminophenol      sulphate 

on  a  Seed  23  emulsion.  This 
developer  (among  others)  in- 
variably showed  wide  departure 
from  the  first  order  relation 


Fig.  32-A 


dD 
— 

at 


(Deo  -  D).       The   open   circles   in  Fig.  32A  show 


the  observed  densities.  Using  data  from  the  smoothed  curve 
through  these  points,  values  of  log  -^ — ITp~  were  comPuted 

for  several  estimates  of  D  «> ,  and  these  were  plotted  against 
the  corresponding  times  of  development  in  Fig.  32B.  The 
value  of  Z)oo  used  is  indicated  on  each  curve.  It  is  evident 
that  a  value  still  lower  than  Dm  =  2.00  is  required  to  produce 
a  straight  line  over  any  range.  Referring  to  the  data  obtained 
it  is  seen  that  this  value  for  the  density  is  reached  after  about 
three  minutes'  development,  and  is  much  exceeded  later. 
The  value  2.00  or  less  is  therefore  wrong,  and  when  examined 
in  detail  the  method  is  found  not  to  apply.  On  plotting 

values  of  log  -=r — °°   _  against  log  /,  a  very  reasonable  value, 
D  co  — -D 

89 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


D  oo  =  2.80,  gives  a  straight  line  over  the  entire  range  observed. 
Fig.  32C  shows  this  and  the  effect  of  using  too  high  or  too  low 
values  of  D  m  .  For  the  value  D  m  =  2.80,  therefore,  the  relation 


is: 


Fig.  32-B 


Fig.  32-C 


tf  (log/  -logO    °log   no°n> 

LJ  co  —  D 

in  which  the  constants  are  as  follows: 
K   =  0.58; 
Da,  =  2.80; 
log/0   =    -1.05; 
/0    =  .35. 
Putting    the    equation    above    in    the    exponential    form 


D    =   Deo    (1      - 


—  * 


and    computing    densities    by 


means  of  it,  with  the  constants  indicated,  the  points  in  Fig. 
32a  shown  by  black  dots  are  obtained.  This  agrees  very  well 
with  the  results  obtained.  Obviously,  it  is  unnecessary  to  go 
to  the  additional  labor  of  computing  densities,  since  the  curve 


of  log 


plotted  against  log  t  indicates  the  nature  of  the 


D  co  — 
agreement. 

Several  experiments,  detailed  in  Table  15  show  the  possi- 
bilities of  the  values  of  D  m  as  computed  being  reached  on 
longer  development. 

90 


THE  THEORY  OF  DEVELOPMENT 


TABLE   151 


T  dev.  Min. 

Special 
Emulsion 

See  30 

Experiment 
108 
Paramino- 
phenol 

D 

Experiment 
124 
Pyrogallol 

D 

Experiment 
126 
Hydroqui- 
none 

D 

Experiment 
135 
Monomethyl 
paramino- 
phenol 
D 

Experiment 
136 
Toluhydro- 
quinone 

D 

Experiment 
140 
Paramino- 
phenol 

D 

0.5 
1 

0 
0.52 

0.52 
1.00 

0 

0.26 

0.60 
1.06 

0.24 
0.77 

0.25 
1.58 

2 
4 

1.12 
1.66 

1.66 
2.38 

1.12 
2.00 

1.66 
2.24 

1.42 
2.20 

1.04 
1.53 

6 

•   8 

1.97 
2.12 

2.77 
2.96 

2.52 
2.85 

2.52 
2.67 

2.66 
2.98 

1.80 
1.98 

10 
15 

2.27 
2.54 

3.06 
3.26 

3.06 
3.32 

2.79 
3.00 

3.20 
3.48 

2.12 
2.43 

20 

25 

2.72 
2.82 

3.36 
3.43 

3.40 
3.48 

3.10    .. 
3.21 

3.62 
3.76 

2.67    * 
2.87 

30 

2.86 

3.60 

3.02 

Computed 

3.00 

4.00 

3.80 

3.60 

4.40 

4.20 

The  values  of  D  co  appear  very  reasonable  in  all  cases  except 
perhaps  the  last  two.  However,  the  densities  are  still,  after 
thirty  minutes'  development,  increasing  at  a  fair  rate.  In 
the  last  case  (Experiment  140)  the  increase  from  the  beginning 
is  very  gradual.  There  were  isolated  cases  in  which  the 
difference  between  the  highest  observed  density  (usually  after 
thirty  minutes'  development)  and  the  computed  Dm  was 
rather  large.  In  general,  the  evidence  is  so  strong  that  the 
few  experiments  giving  such  differences  are  thought  to  be 
either  erroneous  or  exceptions  due  to  relatively  unimportant 
phenomena.  The  computed  values  are  subject  to  an  error 
of  between  five  and  ten  per  cent.  Aside  from  this  error 
there  is  that  due  to  the  difficulty  of  measuring  high  densities 
with  accuracy,  so  that  the  observed  densities  for  long  times  of 
development  are  less  reliable.  The  lower  densities  cannot  be 
used  because  of  the  fog  error. 

In  the  succeeding  chapters  the  equation  D  = 
D  CG  (1  —  e  ~~K  log'//o)  will  be  applied  in  determining  develop- 
ment characteristics,  and  it  is  considered  that  in  addition  to 

1  All  developers  M/20,  with  50  grams  of  sulphite  and  50  grams  carbonate  per  liter. 

91 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

the  above,  the  data  given  there  support  this  equation.  This 
seems  to  be  the  simplest  equation  which  can  describe  the 
development  process  with  any  degree  of  accuracy.  No  doubt 
it  will  be  possible  to  find  a  more  accurate  expression,  but  this 
will  involve  the  use  of  correction  factors  or  constants  unknown 
at  the  present  time,  as  in  Sheppard's  equation  (equation  20, 
page  79).  The  use  of  one  more  constant  than  contained  in 
our  equation  above  necessitates  separate  experimental  work 
for  the  determination  of  the  new  constant  or  one  of  the  others. 

The  following  form  has  been  suggested  : 

D   =  £>oo   (1    -  e   -*<Mo)6).  (30) 

For  X-ray  exposures  and  in  certain  other  cases  this  was  found 
of  somewhat  wider  application  than  the  form  we  have  used. 
But  it  contains  an  additional  constant  b,  which  requires  that 
one  of  the  constants  be  determined  by  experiment.  t0  will 
be  most  convenient,  since  it  represents  the  abscissae  of  the 
intersection  of  the  D-t  curve  with  the  time  axis.  Equation 
30  becomes,  in  the  log  form 

log  K  +  b  log  (t  -  O  =  log  log       Dco  (31) 

D  oo       U 

from  which  is  obtained 

(Dm-D).  (32) 


By  use  of  equation  31   the  constants  may  be   evaluated. 

Log  log  -=r  —  °°         is  plotted  against  log  t  for  a  straight  line  in  a 
D  oo     D 

manner  analogous  to  that  already  used.  The  slope  of  this 
straight  line  is  5,  and  the  ordinate  at  log  /  =  0  will  be  log  K', 
t0  is  obtained  as  indicated  above.  The  entire  process  is  some- 
what more  lengthy  than  desirable. 

Twenty  or  more  cases  of  widely  different  character  were 
computed  by  both  equation  28  (Nietz)  and  equation  30 
(Wilsey).  The  following  table  gives  the  results  of  the  compar- 
ison, the  experiments  with  bromide  added  to  the  developer 
being  withheld  for  the  time  being. 

In  Experiments  132  and  145,  50  gm.  of  sulphite  per  liter 
were  used,  as  before,  but  no  sodium  carbonate.  The  concen- 
tration of  the  developing  agent  was  M/20.  The  emulsion 
used  was  Seed  30.  All  the  computations  are  for  the  standard 
exposure. 

92 


THE  THEORY  OF  DEVELOPMENT 


TABLE  16 


Experiment 
Number 

Developer 

(Wilsey) 

(Nietz) 

£>co 

K 

b 

Z)oo 

K 

129 

130 

132 
135 
137 
145 

133 
136 
144 
140 

Dichlorhydroquinone  
Paramethylamino  orthocresol 
sulphate  .  .          

3.60 
4.00 
1.60 
3.60 
4.00 

3.60 
3.80 
4.00 
3.40 
4.20 

.50 
.65 
.08 
.49 
.28 

.36 
.39 
.28 
.35 
.23 

.42 
.32 
.78 
.47 
.62 

.52 
.46 
.74 
.72 
.50 

3.60 
4.00 

1.78 
3.60 
4.00 

3.60 
3.80 
4.40 
3.80 
4.20 

.53 
.60 

.34 
.58 
.72 

.55 
.68 
.63 
.66 
.30 

Paraphenylene    diamine    hy- 
drochloride  (no  alkali)  
Monomethylparaminophenol 
sulphate 

Paramino  methylcresol  hydro- 
chloride  . 

Diaminophenol  hydrochloride 
(no  alkali) 

Dibromhydroquinone  
Toluhydroquinone  
Bromhydroquinone  
Paraminophenol  hydrochloride 

These  results  show  that  the  two  equations  yield  practically 
the  same  value  for  the  equilibrium  constant  D  m  .  As  would  be 
expected,  K  varies  widely  in  some  cases,  Wilsey 's  constant  b 
influencing  the  variation.  t0  is  not  recorded  as  it  is  deter- 
mined experimentally  in  Wilsey's  method  and  in  the  other  is 
an  empirical  constant  larger  than  the  observed  t0.  Wilsey's 
equation  has  the  advantage  that,  although  more  complex  and 
therefore  more  cumbersome,  it  more  nearly  describes  the 
development  process  from  beginning  to  end.  It  generally 
gives  nearly  the  same  values  for  D  «>  as  the  form  D  =  D  m 
( 1  -  e  ~K  log  '/'<>)  and  in  addition  fits  the  beginning  of  the 
reaction  somewhat  better  (beyond  a  small  initial  period  of 
acceleration).  In  the  experiments  detailed  in  Table  16, 
equation  30  fitted  the  data  from  two  or  three  minutes  on,  as  a 
rule.  It  is  somewhat  difficult  to  attach  much  physical 
significance  to  the  constants  of  this  equation. 

CONCLUSIONS 

In  Table  17  the  various  velocity  equations  under  discussion 
are  summarized.  In  brief,  the  findings  for  each  case  are: 

I.  The  simple  form  describes  the  early  stages  of  the  reaction, 
and  these  only  under  limited  conditions.  It  is  necessary  that 
the  time  of  appearance  be  very  short  and  that  the  reaction 
be  one  which  does  not  damp  itself  quickly — i.  e.,  does  not 
proceed  rapidly  to  nearly  its  maximum.  A  density- time 
curve  of  nearly  hyperbolic  form  (such  as  often  given  by 
monomethylparaminophenol  sulphate  and  paraminophenol 
hydrochloride)  cannot  be  fitted  except  for  a  very  short  range 
of  time. 

93 


o.2 
o  fc-p 


c 

OJ 

I 

X 

W 


c      ^ 
o  olg 

"^  ^    rt 

sisS 

!_,    -^   ^^ 

o  c^co 
U 


"H 

a 

a 

cu 

CA! 


THE  THEORY  OF  DEVELOPMENT 

II.  Much  more  satisfactory  than  I,  but  not  generally  appli- 
cable, it  nearly  always  fails  to  fit  the  data  in  the  later  stages. 
This  indicates  that  photographic  development  shows,  after  a 
time  at  least,  departures  from  the  first  order  reaction  law. 

Equation  II  is  useful  especially  in  the  determination  of  t0, 
which,  computed  by  this  equation,  is  practically  the  time  of 
appearance  and  gives  more  reliable  results  than  could  be 
obtained  by  the  visual  method. 

III.  This  equation  is  of  general  application.    It  fits  practi- 
cally all  cases  beyond  the  initial  stage  and  is  easily  applied 
to  the  data.     /0    is  an  empirical  constant.     In  some  experi- 
ments equation  III  yields  values  of  D  m  which  are  quite  high 
compared  with  those  observed  on  long  development,  but  it  is 
quite  possible  that  development  continues  for  hours.     Experi- 
mental  verification   of   the   value   of   the   maximum   density 
was  obtained  in  nearly  all  cases.     In  some  doubtful  experi- 
ments development  probably  was  not  long  enough   and    the 
densities     obtained     were    too    high    to    permit    of    accurate 
measurement. 

The  fact  that  equation  III  indicates  that  the  velocity  is 
inversely  proportional  to  the  time  is  not  satisfactorily  ex- 
plained. The  writer  assumes  that  various  complex  phenomena 
affect  the  result  in  such  a  way  that  \/t  in  the  velocity  equation 
represents  a  close  approximation  to  the  real  function.  Further 
study  would  be  required  to  determine  the  true  relation. 

For  general  comparisons  equation  III  is  believed  to  be  quite 
the  most  satisfactory  form  from  the  standpoint  both  of 
convenience  and  of  accuracy. 

IV.  Equation  IV  sometimes  holds  over  a  wider  range  than 
equation  III  and  is  generally  equally  satisfactory,  though  it  is 
not  so  easily  applied.     One  of  the  constants  must  be  deter- 
mined experimentally,  and  doing  this  for  t0  simplifies  the  meth- 
od.    As  an   empirical  expression   this  form  most  accurately 
describes    the    relation    between    time    of    development    and 
density  developed. 

V.  Equation   V   cannot   be   applied    because   of    the   large 
number  of  unknown  factors  involved. 

Glancing  down  the  column  marked  "First  Derivative,"  in 
Table  17,  it  is  seen  that  the  velocity  function  has  been  made 
more  and  more  complex.  More  correction  factors  have  been 
applied  to  account  for  the  phenomena  occurring.  No  doubt 
we  should  find  if  we  could  apply  equation  V  that  it  would  fit 
the  data  more  perfectly  than  the  preceding  forms,  as  the 
corrections  are  larger  in  number.  Equation  V  was  deduced 

95 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

for  development  with  ferrous  oxalate  by  the  use  of  certain 
simplifying   assumptions. 

For  alkaline  development,  which  is  so  much  more  complex, 
any  number  of  other  involved  equations  might  be  set  up,  none 
of  which  would  be  more  than  a  purely  empirical  expression. 
Since  either  equation  III  or  equation  IV  supplies  the  need, 
and  apparently  gives  a  reliable  indication  of  the  end-point 
of  the  reaction,  it  seems  justifiable  to  apply  them  to  the  data 
obtained.1 

1  Since  this  was  first  written,  an  equation  based  on  the  inclusion  of  terms  for  a  paralysing 
action  of  reaction  products  has  been  developed  by  Sheppard  (Phot.  J.,  59:  135.  1919) 
and  is  now  being  investigated. 


96 


CHAPTER  VI 

VELOCITY  OP  DEVELOPMENT  (Continued) 

Maximum  Density  and  Maximum  Contrast  and 

their  Relation  to  Reduction  Potential  and 

other  Properties  of  a  Developer 

CHARACTERISTICS  OF  THE  VELOCITY  EQUATION 

The  character  of  the  velocity  equation 

T\    _  Y)        M      p  — Klogt/t0\ 

is  more  or  less  evident  from  inspection  of  the  exponential  and 
logarithmic  forms  and  of  the  derivative,  but  the  interpretation 
of  these  into  photographic  results  is  not  so  clear.  For  this 
reason  a  brief  analysis  is  made.  If  /  =  /0,  D  =  0.  When 

The  factor   (1   —  e~~K*~ 


t  = 


D  =  D 


D 


and 


therefore  expresses  the  fraction  developed  at  the  time  t. 

The  effect  of  changing  each  of  the  three  variables,  K,  t0  and 
D  oo  ,  one  at  a  time,  is  as  follows : 

The  higher  the  value  of  K,  the  greater  the  density  in  the 
time  /,  and  the  greater  the  fraction  developed. 

For  variable /0,  the  fraction  developed  at  a  given  time  be- 
comes less  with  increasing  t0.  The  entire  curve  (D  —  t)  is 
shifted,  each  density  being  displaced  horizontally  by  the 
increase  in  t0.  Hence  the  density  produced  in  a  given  time  is 
decreased  if  t0  is  increased. 

Increasing  D  co  produces  greater  density  in  a  given  time  of 
development.  The  fraction  developed  is  always  the  same  for 
equal  times. 


D-t  curves  K  =  .10  (bottom), 
.30,  .50,  .80 

Fig.  33 


97 


D-t  curves  for  t0  =  .1,  .5,  1.0, 
2.0,  3.0  and  4.0  (bottom) 

Fig.  34 


35. 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

These  relations  are  shown  respectively  by  Figs.  33,  34,  and 


D 


shows 


The  logarithmic  form  K  (log  t  —  log  t0)   =  log          _ 
obvious  relations  already  described.  °° 

The  derivative  is 

f  •  f »-  -  •»• 

For  the  curve  in  Fig.  34,  where  t0  =  1.0,  K  =  0.3  and  Dm  =3.0, 
the   velocity  varies   with  time  as   shown   by  the  continuous 

line  in  Fig.  36,  in   which  the  ordinate  is  —  or  the  velocity. 

at 

These  values  represent  a  typical  case.  In  practice  there  is  the 
period  of  induction,  shown  by  the  dotted  line. 


D-t  curves  for  D  co=1.6  (Bottom), 
2.0,  2.5,  3.0  and  4.0 

Fig.  35 


Velocity  curve 

Fig.  36 


One  of  the  chief  characteristics  of  this  equation  is  the  length 
of  time  required  to  reach  nearly  complete  development.  For 
example,  in  Fig.  35  the  fractions  developed  are  as  follows: 

t  (1    -g-Kiogi/<o)    =  fraction 

developed 


2  mm. 

4  min. 

6  min. 

8  min. 
10  min. 
15  min. 


.43 
.57 
.63 
.67 
.70 
.74 


The  time  required  for  a  definite  fraction  to  be  developed  may 
be  found  by  equating  (1  -  e~Kl°8tlt°)  to  the  desired 
fraction,  inserting  the  values  of  K  and  t0  and  solving  for  /.  For 

any  fraction  a  the  time  /  =  t0e  K  log  i=£    For    the    theoretical 
curve    in    Fig  34    (/0    =    1.0,  K   =  0.3,  and   Dm    =  3.0),    for 

98 


THE  THEORY  OF  DEVELOPMENT 

which  the  velocity  curve  is  shown  in  Fig.  36,  the  time  for 

ninety  per  cent  development  is  accordingly  t0e  ~ir  =(1.0)  e  ~~J~ 

=  2,140  minutes.  The  higher  the  value  of  K  and  the 
lower  the  value  of  t0,  the  shorter  the  time  required.  In  most 
cases  the  time  for  ninety  per  cent  development  varies  from 
thirty  minutes  to  two  or  three  hours. 


DETAILS  OF  THE  EXPERIMENTS 

The  procedure  has  already  been  outlined.  The  density- 
time  curves  secured  for  a  standard  value  of  the  exposure 
(standard  log  E)  were  such  that  in  all  cases  the  densities  lay 
well  up  on  the  plate  curve.  Other  results  showed  that  under 
these  conditions  the  fog  error  is  eliminated.  In  general,  the 
density-time  curve  for  these  conditions  gives  the  most  reliable 
photographic  data  which  can  be  secured.  It  is,  of  course, 
affected  by  any  erratic  behavior  of  the  developer,  but  usually 
less  so  than  other  data  for  the  same  emulsion  and  developer. 

In  all  cases  the  times  of  development  ranged  from  that 
necessary  to  produce  the  first  visible  density  to  at  least  15 
minutes  and,  in  the  majority  of  cases,  25  to  30  minutes  or 
more.  As  a  rule  the  values  of  the  constants  D  «> ,  K,  and  t0 
were  found  for  the  particular  equation  which  fitted  the  data 
over  the  maximum  range  from  the  longest  observed  time  back 
toward  the  beginning.  In  most  cases  there  was  little  doubt  as 
to  these  values.  The  average  error  in  drawing  a  new  curve 
and  recomputing  D  m  ,  or  in  a  repetition  of  the  experiment  with 
an  ordinary  developer  and  emulsion,  is  between  five  and  ten 
per  cent.  In  some  cases  the  developer  or  the  emulsion  or  both 
reacted  in  unusual  ways,  and  the  results  were  of  little  value. 
We  believe  the  results  given  below  to  be  as  accurate  as  any 
it  is  possible  to  secure  under  like  conditions. 

VARIATION    OF    MAXIMUM   DENSITY   WITH   EXPOSURE 

If  the  density-time  curves  are  drawn  for  different  values 
of  log  E  for  a  given  developer  and  emulsion  and  the  maximum 
density  computed  for  each,  different  values  of  Deo  result 
which,  plotted  against  the  logarithms  of  the  corresponding 
exposures,  give  a  new  plate  curve  for  the  equilibrium  condition. 
This  is  illustrated  in  Fig.  37.  Each  point  represents  a  com- 
putation of  Das  from  a  density- time  curve  at  the  indicated 
log  E  value.  The  point  M  can  be  determined  separately  by 
methods  already  explained,  it  representing  the  common  inter- 

99 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


Fig.  37 


Fig.  38 


section  point  of  the  H.  and  D.  curves  for  the  given  conditions. 
In  Fig.  37  the  curves  intersect  on  the  log  E  axis  as  usual,  and 
the  value  of  a  (the  log  E  coordinate  of  the  point  of  intersection) 
is  0.12.  Consequently  a  straight  line  or  plate  curve  may  be 
drawn  from  M  through  the  series  of  maximum  densities,  as 
shown.  Increasing  fog  error  prevents  the  locating  of  more 
points  for  the  lower  log  E  values.  From  other  information 
and  a  consideration  of  the  plate  curves  it  does  not  seem  logical 
to  take  a  value  of  log  E  much  lower  than  1.4. 

The  curve  shown  is  for  M/20  paraminophenol  hydrochloride 
on  a  Seed  30  emulsion,  a  was  determined  from  a  number  of 
experiments,  using  various  concentrations  of  bromide. 

Fig.  38  represents  a  similar  result  from  M/20  dibromhydro- 
quinone  on  a  fast  emulsion.  Here  a  is  obtained  from  but  one 
determination  with  no  bromide,  and,  therefore,  is  not  so 
accurate  as  the  preceding  value. 

Such  experiments  show  that  within  reasonable  limits,  the 
plate  curve  for  infinite  development  may  be  drawn.  Also,  this 
method  increases  the  accuracy  of  the  determination  of  D  oo  at 
any  particular  value  of  log  E. 

MAXIMUM  CONTRAST  (  f  co  )  AND  A  NEW  METHOD  FOR  ITS 
DETERMINATION 

It  is  impossible  to  treat  separately  and  in  a  definite  order  all 
phases  of  the  present  problem.  For  convenience  in  presenting 
the  data,  the  maximum  contrast,  y  oo  ,  will  be  discussed  here. 

100 


THE  THEORY  OF  DEVELOPMENT 

This  term  (Y  oo )  requires  careful  interpretation.  Y  oo  is 
the  theoretical  contrast  reached  on  infinite  development,  or 
the  slope  of  the  plate  curve  when  development  has  reached 
equilibrium.  In  practice  this  is  never  attained,  since  all 
developers  and  emulsions  give  appreciable  fog  on  prolonged 
development,  and  the  fog  is  greater  the  lower  the  density  of 
the  image.  Hence  the  lower  portion  of  the  straight  line  of  the 
plate  curve  in  Fig.  38  will  be  raised  by  fog,  the  contrast  thus 
being  lowered.  But  the  image  tends  to  give  the  contrast 
indicated  by  the  lines  in  Figs.  37  and  38  and  this  value  is  the 
characteristic  constant  for  the  given  condition.  The  highest 
contrast  which  can  be  obtained  practically  will  be  reached  at 
some  intermediate  time  and  will  then  decrease,  the  maximum 
being  always  lower  than  Y  oo  as  defined.  Fig.  39  shows  these 

relations  for  a  developer  giving 
bad  fog  on  prolonged  develop- 
ment. YA  is  the  contrast  ob- 
tained. At  about  eight  and 
one-half  minutes'  development 
YA  is  nearly  equal  to  Y  oo , 
which  was  found  by  the  method 
described  below.  The  devel- 
oper used  was  M/20  hydro- 
quinone  without  bromide.  With 
Fig.  39  certain  developers,  and  always 

when    bromide    is    used,    the 

maximum  value  of  YA  may  continue  for  a  long  time,  the 
period  of  decrease  being  delayed.  Thus  over  an  observed 
range  of  ten  to  fifteen  minutes  the  Y  •-  t  curve  may  be  an 
exponential  of  the  same  type  as  the  D  -  t  curve. 

Where  it  is  possible  to  draw  the  curve  for  the  plate  at 
maximum  development,  as  in  Figs.  37  and  38,  Y  oo  can  be 
determined  from  the  slope  of  the  straight  line.  If  this  can 
not  be  done,  it  may  be  computed  as  follows:  The  relation 
between  density  and  gamma  was  expressed  as 

D   =  Y  (log  E   -  a)  +  b. 

From  data  on  the  D  -  Y  relation,  especially  with  bromide, 
where  upon  prolonged  development  Y  oo  is  closely  approached, 
there  is  every  reason  to  believe  that  this  relation  holds  at  the 
limit; — that  is, 

Dn    =  YOO  (log  E  -  a)   +  b;  (33) 

from  which 


101 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Consequently,  Too  may  be  calculated  if  Dm  is  known  (from 
a  velocity  curve  at  some  particular  value  of  log  E)  and  the 
values  of  a  and  b  are  also  known.  In  the  complete  study  of  an 
ordinary  developer  all  these  can  be  determined  with  a  fair 
degree  of  accuracy. 

In  Fig.  38,  for  example,  the  value  of  Dm  at  log  E   =  2.4  is 

4-  70 

4.20,  b  =  0,  and  a  =  -0.60.  Therefore,  y  oo  =240+060  =  L4°' 
which  the  figure  also  shows. 

In  Fig.  37,  log  E  =  1.8  (on  the  straight  line  portion).     D  oo   =3.20, 

b=0  and  a  =  0.12.    Therefore,  y  oo  =1  o^'™*    o  =  i-92- 

l.oU    —   U.12 

As  previously  stated,  D  m  is  usually  determined  more  ac- 
curately than  a.  Hence  the  accuracy  of  y  oo  is  governed 
largely  by  the  accuracy  of  a.  In  Fig.  37,  a  is  well  determined. 
In  Fig.  38  it  is  the  result  of  but  one  set  of  observations. 

Some  advantages  of  the  above  method,  as  well  as  its  further 
applications,  are  discussed  in  a  later  chapter.  (See  Chapter 
X.) 


VARIATION  OF  DOS    AND  y  oo    WITH  THE  DEVELOPER 

From  the  chemical  standpoint  Dm  is  more  important  than 
y  oo ,  as  a  constant,  the  latter  being  merely  a  consequence  of 
the  former  and  of  the  relative  location  of  the  intersection  point 
of  the  plate  curves.  From  the  photographic  standpoint  yoo 
and  the  maximum  value  of  yA  are  of  greater  importance,  as 
they  are  more  obvious  indicators  of  the  character  of  the 
emulsion  and  of  the  developer.  In  the  present  instance  we  are 
interested  mainly  in  the  relations  for  the  density  at  equilibrium, 
though  results  for  the  contrast  are  included. 

As  a  result  of  the  experimental  work,  the  view  that  the 
inertia  point,  the  value  of  D  m  for  fixed  exposure,  and  y  oo  are 
fundamental  constants  of  an  emulsion  must  be  abandoned.  It 
has  been  shown  that  the  inertia  may  change  with  the  developer. 
Sheppard  and  Mees  also  found  this,  but  did  not  find  the 
variation  great,  few  developers  being  used.  Aside  from  the 
work  of  Sheppard  and  Mees,  very  little  has  been  done  on  the 
relations  oi  D  m  and  y  co  as  here  considered.  There  is  no 
doubt  that  some  developers  can  reduce  more  silver  for  the 
same  exposure,  and  to  greater  or  less  degrees  of  contrast,  than 
others.  Consequently,  Dm  and  y  oo  are  not  fixed  constants 

102 


THE  THEORY  OF  DEVELOPMENT 

for  an  emulsion.  They  may  be  used  as  such  only  when  a 
certain  developer  is  used,  the  variations  then  being  assumed 
as  due  to  the  emulsion. 

The  available  evidence  on  these  equations  is  given  below. 
It  is  quite  conclusive  in  many  respects,  and  the  continual 
recurrence  of  certain  relations  throughout  the  work  strengthens 
the  hypotheses. 

In  the  following  results  D  «>  and  K  were  found  by  means  of 
the  equation  D=  D  m  (1  -e—Klost/t°)  applied  to  the 
D  —  t  curve  for  a  fixed  exposure,  a  and  b  were  found  from 
D  -  y  curves  for  the  same  exposure,  and  y  m  was  then 
computed  from  equation  34. 

Experimental  conditions  were  constant  for  each  set. 

Table  18  gives  the  results  of  experiments  on  an  ordinary 
emulsion  of  medium  speed.  Values  of  the  reduction  potentials 
C^Br)  of  the  developers  as  previously  found,  are  included  for 
convenience. 

TABLE  18 

DEVELOPER  7TBr  D  «>  J  ^ 

M/25     Bromhydroquinone 21  3.7  2.29 

M/20  Monomethylparaminophenol  sulphate  ...  20 

M/20     Chlorhydroquinone 7  2.7  1 . 62 

M  /20     Paraminophenol  hydrochloride 6  3.2  1 . 99 

M/20     Toluhydroquinone 2.2  373  1.75 

M/20     Paraphenylglycine   1.6  2^8  1 .55 

It  is  evident  here  that  the  maximum  density  D  m  and  the 
maximum  contrast  y  oo  show  a  marked  tendency  to  increase 
with  increasing  reduction  potential.  It  was  concluded  from 
these  data  that  the  relation  would  hold,  but  further  work 
showed  exceptions  to  the  rule.  Hydroquinone,  for  example, 
though  a  developer  of  high  bromide  sensitiveness,  (i.  e.,  low 
reduction  potential),  can  produce  high  maximum  density  and 
contrast.  Consequently,  as  before  when  an  attempt  was  made 
to  give  a  classification  on  the  basis  of  reduction  potential,  these 
exceptions  show  that  the  reduction  potential  is  not  always  the 
chief  governing  characteristic.  But  we  believe  that  the 
reduction  potential  often  conditions  the  result,  and  that  the 
general  trend  is  in  the  direction  of  the  results  shown  in  Table 
18, 

Table  19  gives  the  results  of  four  developers  of  Special 
Emulsion  IX,  a  fast  ordinary  emulsion  on  patent  plate  glass. 


103 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


TABLE   19 


DEVELOPER 


7T, 


M/20  Pyrogallol 16  3.90  1.71 

M/20  Dimethyl  paraminophenol  sulphate 10  2.80  1.47 

M/20  Paraminophenol  hydrochloride 6  3.00  1.40 

M/20  Paraphenylglycine 1.6  3 . 40  1.32 

Table  20  gives  the  data  from  twenty  experiments  on  emul- 
sions for  some  of  which  the  speed  data  are  given  in  Table  10, 
Chapter  IV.  The  results  from  three  developers  in  Table  19 
are  included. 

TABLE  20 

Variation  of  D  <»,  7  oo    and  K  with  emulsion  and  developer 
I     M/20     Pyrogallol 

II     M/20     Dimethylparaminophenol  sulphate 
III     M/20     Paraminophenol  hydrochloride 


EMULSION 

I 

II 

III 

Doo 

'YoO 

K 

£>oc 

7°o 

K 

£>oo 

'Yoo 

K 

Special  Emulsion  IX  
Special  Emulsion  VIII  
Special  Emulsion  XII  
Special  XIII  
Emulsion  3533  
Special  Bromide  XIV  
Film  Special  Emulsion  XV  

^Br  - 

3.90 
3.50 
3.60 
4.00 
4.00 
5.00 

1.71 
3.58 
1  .90 
5.7 
1  .22 
5.9 

.53 
.31 
.65 
.31 
.57 
.38 

2.80 
2.50 
2.80 
4.00 
3.20 
3.60 
2.80 

1  .47 
3.30 
1  .76 
5.9 
1.18 

1.84 

.64 
.36 

.45 
.34 
.61 
.3( 
.27 

3.00 
2.10 
3.15 
3.50 
4.20 
3.70 
2.60 

1.40 
1  .98 
1.85 
5.6 
1  .84 
3.40 
2.00 

.58 
.33 
.50 
.21 
.40 
.26 
.56 

16 

10 

6 

In  analyzing  the  table  and  comparing  the  results  it  is  seen 
that  of  the  three  developers  at  the  same  concentration,  pyro- 
gallol  can  reduce  the  most  silver  for  the  same  exposure.  This 
is  an  indication  that  on  the  average  it  probably  develops 
greater  theoretical  contrast.  M/20  paraminophenol  hydro- 
chloride  on  Emulsion  3533  seems  to  be  an  exception  to  both 
rules.  The  relation  between  paraminophenol  and  dimethyl- 
paraminophenol  is  somewhat  indefinite.  These  developers  are 
nearer  each  other  in  reduction  potential  than  is  the  higher  to 
pyrogallol,  and  they  resemble  each  other  in  chemical  proper- 
ties to  a  much  greater  extent  than  either  resembles  pyrogallol. 
Consequently  the  above  results  are  not  surprising.  Other 
results  to  be  given  below  show  that  developers  differing  widely 
in  their  chemical  nature  generally  develop  to  different  degrees, 
but  that  compounds  which  react  similarly  do  not  differ  much 
in  this  respect. 

To  test  this  hypothesis  further  equivalent  concentrations  of 
a  number  of  reducing  agents  were  used  on  the  same  emulsion. 
In  Table  21,  these  are  arranged  in  order  of  D  &  ,  beginning 
with  the  highest.  If  two  developers  give  the  same  Deo,  the 

104 


THE  THEORY  OF  DEVELOPMENT 

one  with  the  higher  K  and  lower  t0  is  placed  first,  it  being 
assumed  that  in  general  the  faster  is  the  more  powerful. 
Values  of  D m  ,  Too ,  K,  and  /0  are  included. 

TABLE  21 

Different  developers  on  the  same  emulsion,1  arranged  according  to  values 

of  D-oo 


DEVELOPER 

M/20  Toluhydroquinone  
Diaminophenol  plus  alkali*  .  .  .  . 
Paraminophenol*  

D 

4 

4. 
4. 

oo 

40 

2 
2 

^Br 

2.2 
40. 
6. 

7oo 

1.67 
1.40 
1.84 

K 
.63 
.60 
.44 

1 
0 
1 

t0 

.35 
6 
0 

Paramino-metacresol  
Methylparamino-orthocresol  .  .  . 

Pyrogallol*  
Chlorhydroquinone*  

Hydroquinone*  

4 
4 

4 
4 

3 

0 
0 

0 
0 

8 

9. 

23. 

16. 

7. 

1. 

1.33 
1.26 

1.22 
1.82 

1.26 

.72 
.60 

.57 
.52 

.95 

1 

0 

1 

1 

.24 
.33 

.78 
.3 

.80 

Dibromhydroquinone  

Paramino-orthocresol  
Bromhydroquinone  
Eikonogen  
Monomethylparaminophenol*.  . 
Diaminophenol,  no  alkali  
Pyrocatechin  
Dichlorhydroquinone  
Edinol  

3 

3 
3 
3 
3. 
3 
3 
3. 
3 

8 

8 
8 
8 
6 
6 
6 
6 
6 

8. 

7. 
21. 

20.  ' 
ll' 

1.27 

1.27 
1.73 
1.43 
.50 
.63 
.68 
.29 
.22 

.80 

.70 
.66 
.47 
.58 
.55 
.52 
.53 
.46 

0 
0 

1 
1 

1 

.80 

.87 
.27 
.7 
.70 
.36 
.60 
80 
.9 

Phenylhydrazine,  no  alkali 3.5          1.0      03     8.5 

Dimethylparaminophenol 3.2       10.0     1.18        .61     0.75 

Ferrous  oxalate* 3.1         0.3     1.29        .55     0.97 

Benzyl  paraminophenol  less  than 

(Duratol) 2.4  5       0.98        .34     2.27 

Paraphenylene  diamine 1.7         0.4     0.58        .34     2.10 

Of  the  developing  agents  in  Table  21,  those  marked  with  an 
asterisk  were  of  high  purity,  the  others,  excepting  Edinol, 
Duratol,  and  Eikonogen,  which  were  the  commercial  product, 
were  somewhat  better  than  commercial  purity. 

This  table  does  not  by  any  means  show  that  Dm  always 
varies  with  the  reduction  potential,  if  the  latter  as  previously 
measured  is  considered.  But  by  this  method,  developers  may 
be  compared  on  a  basis  which  is  more  or  less  independent  of  the 
observer,  the  degree  of  development,  and  numbers  of  special 
factors,  and  it  is  quite  certain  that  several  definite  tendencies 
are  indicated.  These  may  be  summarized  as  follows: 


Seed  30  Emulsion  3533 


105 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

D  co  and  y  a>  for  a  single  emulsion  may  vary  greatly  with 
different  reducing  agents. 

The  value  of  the  equilibrium  density,  D  m ,  tends  to  be 
greater  the  higher  the  reduction  potential  of  the  developer. 
Exceptions  to  this  rule  may  be  accounted  for  in  a  number  of 
ways,  on  none  of  which  ther.e  is  definite  information.  (See 
effect  of  sulphite  on  the  maximum  density  obtained  with 
hydroquinone,  Chapter  IX.) 

y  oo  shows  an  unordered  variation  with  any  of  the  proper- 
ties of  the  reducing  agents.  The  lowest  values  are  obtained 
for  developers  of  the  lowest  reduction  potential,  but  this  re- 
lation does  not  hold  with  higher  values.  The  intersection 
points  of  the  H.  and  D.  curves  show  similar  unsystematic 
shifting.  Because  the  speed  of  the  plate  is  a  function  of  some 
other  property  than  the  reduction  potential  of  the  reducing 
agent,  y  oo  is  also.  For  developers  giving  about  the  same 
plate  speed,  y  oo  tends  to  be  higher  with  increasing  potential. 

The  unsubstituted  aminophenols  stand  at  the  head  of  the 
list  in  Table  21,  next  the  hydroxybenzenes  and  their  halogen 
substitution  products,  and  the  amines  are  at  the  bottom. 

Hydroquinone  and  its  mono-  and  dichlor-  and  brom- 
substitutions  seem  to  be  nearly  identical  in  this  classification, 
though  their  reduction  potentials  vary  greatly.  This  may  be 
because  the  mechanism  of  their  oxidation  is  the  same,  and 
that  other  conditions  also  are  similar,  these  masking  any 
effect  of  reduction  potential. 

Most  cases  which  show  a  systematic  variation  of  D  oo  with 
reduction  potential  also  show  systematic  variation  in  what  is 
erroneously  termed  the  "rapidity" — that  is,  the  time  required 
to  develop  a  definte  intermediate  density.  If,  for  example, 
we  note  the  densities  developed  in,  say,  two  minutes  for  each 
case,  these  will  tend  to  be  in  the  same  order  as  the  values  of 
D  oo  •  This  is  evident  from  the  character  of  the  equation 

D    =    Z>oo     (1    -  e-K]ost/t°),     (see    also    Fig.    35),     since    if 

K  and  t0  are  nearly  constant  the  density  for  a  fixed  time  will 
vary  with  D  oo  .  From  the  data  given  it  will  be  seen  that  the 
variation  in  K  is  not  great  and  that  for  many  compounds  t0 
also  does  not  vary  widely.  Some  of  these  facts  will  be  clearer 
from  the  following  discussion. 

The  analogy  of  the  relations  to  Ohm's  law  may  be  roughly 
illustrated  by  the  experiments  detailed  in  Table  21.  Of 
course  we  should  not  expect  this  relation  to  hold  with  any 
accuracy  since  velocity  is  not  usually  a  reliable  measure  of 

106 


THE  THEORY  OF  DEVELOPMENT 

potential,  but  the  fact  that  it  gives  even  approximately  the 
right  order  for  the  developers  below,  as  we  know  them,  is  inter- 
esting indirect  evidence.  By  analogy 

,,  .     .  Potential 

Velocity  =• 


Resistance 
or 

Potential   =  Velocity  x  Resistance. 

According  to  Nernst  and  others  the  principal  factors  of  the 
resistance  here  are  the  diffusion  phenomena.  For  two  develop- 
ers used  on  the  same  emulsion,  where  the  period  of  retardation, 
shown  by  t0,  and  the  velocity  constant  K  are  each  the  same  for 
both  cases,  the  diffusion  effects  and  minor  factors  of  the 
resistance  may  quite  reasonably  be  assumed  to  be  equal. 
Hence  the  potentials  will  be  directly  proportional  to  the 
velocities  for  these  conditions,  or 

^        *-(n     -m 

Potential          Velocity  dt  t 


X 


Potential          Velocity          dD          K 

Std.  Std.  (D  co  —D} 

dt  std.       /  stdt 

Taking  the  velocities  at  the  time  /  in  both  cases  gives  us  for 

K(Doo  -  D) 
the  above       ,          — =-*      If  Kx  =  K  std.       the  equation  would 

A.    \Lf  co        Lf) 


be  further  simplified,  but  we  have  no  instances  in  which  this 
relation  is  more  than  approximately  true.  Consequently  in 
the  table  below  the  developers  are  grouped  according  to  equal 
retardation  times  and  are  intercompared  by  the  ratios  of  the 
velocities.  No  more  data  were  available  for  this  comparison, 
as  it  is  necessary  to  have  both  t0  and  K  the  same  for  the 
different  developers.  The  values  given  are  for  the  developers 
and  the  emulsions  referred  to  in  Table  21.  All  velocities 
are  computed  for  two  minutes  from  the  derivative  of 
D  =£>oo  (1  -  e-*togf/i.)  ,  -  i.  e.,dD/dt  =  (K/2).  (Dm  -  D). 


107 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


TABLE  22 

Relative  Reduction  Potentials,   Computed  by  Comparison  of  Velocities 
for  Equal  Resistances 

Potential^ 


Potential 


Std. 


dD/dt. 


for  Std. 


All  developers  M/20  except  ferrous  oxalate,  which  is  M/10. 


DEVELOPER 

I 

K 

Doo 

After 
2  minutes 

Velocity  at 
2  minutes 

Relative 
Potential 

Pyrogallol  
Dimethylparaminophenol  
Dichlorhydroquinone  

.78 
.75 
.80 

.57 
.61 
.53 

4.00 
3.20 
3.60 

1  .27 
1  .48 
1.38 

.67 
.52 
.59 

13 
Std.   =  10 
11 

Ferrous  oxalate  
Paraminophenol  

.97 
1  .00 

.55 
.44 

3.10 
4.20 

0.70 
1  .04 

.66 
.70 

5.7 
Std.  =     6 

Dibromhydroquinone  
Paramino-orthocresol  

.80 
.87 

.80 
.70 

3.80 
3.80 

.38 
.40 

.97 
.84 

8 

Std.  =     7 

Paramino-metacresol  
Chlorhydroquinone   
Toluhydroquinone   
Bromhydroquinone  

1  .24 
1  .30 
1  .30 

1  .27 

.72 
.52 
.63 
.66 

4.00 
4.00 
4.40 
3.80 

1.30 
.24 
.42 
.36 

.97 
.72 
.94 
.81 

9.5 

Std.   =     7 
7 
8.4 

The  comparison  is  by  groups,  in  each  of  which  the  condi- 
tions are  approximately  fulfilled. 

Arranging  these  values  in  order  and  comparing  them  with 
those  previously  found  by  the  depression  method  gives  the 
results  in  Table  23. 

TABLE  23 
Relative  Reduction  Potentials 


Pyrogallol 

Dichlorhydroquinone 

Dimethylparaminophenol 

Paramino-metacresol 

Bromhydroquinone 

Dibromhydroquinone 

Paramino-orthocresol 

Chlorhydroquinone 

Toluhydroquinone 

Paraminophenol 

Ferrous  oxalate 

Although  the  above  values  are  not  entirely  consistent,  there 
is  reasonable  evidence  that  the  assumptions  of  equal  resistance 
are  approximately  correct,  and  that  for  such  cases  the  veloci- 
ties calculated  from  the  velocity  function  are  a  measure  of 
the  potentials.  There  is  further  evidence  that  a  developer  of 

*  Not  determined 

108 


From  velocity 

From  previous 

ratios 

data 

13 

16 

11 

* 

10 

10 

9.5 

* 

8.4 

21 

8 

* 

7 

7 

7 

7 

7 

2.2 

6 

6 

5.7 

0.3 

THE  THEORY  OF  DEVELOPMENT 

lower  reduction  potential  reduces  less  silver.  If  bromide  is 
added  to  a  developer,  its  reduction  potential  is  lower  than  if 
no  bromide  were  present;  and  as  its  potential  is  lowered  (more 
bromide  is  added)  the  maximum  amount  of  work  it  can  do, 
measured  by  "the  equilibrium  density,  D  oo  ,  decreases.  The 
systematic  variation  of  D  &>  with  the  reduction  potential  under 
these  conditions  is  easily  understood,  as  no  doubt  the  com- 
plicating factors  which  vary  from  one  developer  to  another  are 
constant  here.  Resistance  factors  due  to  addition  of  bromide 
are  evident  only  in  a  change  in  /0,  not  in  K,  as  will  be  shown 
later. 

It  seems  quite  probable  that  in  many  cases,  comparing  the 
velocities  gives  a  rough  measure  of  the  reduction  potential,  and 
that  the  classification  according  to  the  values  of  the  equilibrium 
point  alone  furnishes  information  in  this  direction.  We  should 
expect  the  more  powerful  developer  to  drive  the  reaction 
farther  in  the  presence  of  its  oxidation  product.  If,  however, 
the  oxidation  products  are  removed  by  side  reactions,  or  if 
other  physical  or  chemical  factors  exert  control  over  the  de- 
velopment process,  the  end  point  and  the  velocity  become  a 
false  measure  of  the  energy.  This  is  probably  what  occurs 
with  hydroquinone  and  some  of  its  substitution  products, 
causing  them  to  develop  as  much  density  finally  as  monome- 
thylparaminophenol,  for  example. 

THE  LATENT  IMAGE  CURVE 

If  different  amounts  of  silver  can  be  reduced  by  different 
developing  solutions,  what  determines  the  limit  to  which  the 
process  can  go?  Can  the  latent  image  be  fully  developed? 
To  these  questions  a  definite  answer  can  not  yet  be  given.  It 
is  not  possible  at  present  to  determine  the  quantity  of  latent 
image  present  in  an  emulsion  which  has  been  affected  by  a 
definite  quantity  of  energy.  However,  a  few  generalizations 
concerning  the  relations  between  the  developer  and  the 
quantity  of  latent  image  developed  may  be  given. 

The  grain  is  considered  the  unit  of  the  latent  image.  If  a 
single  nucleus  exists  in  the  grain,  the  latter  is  developable. 
That  is,  it  requires  photochemical  change  of  but  one  molecule 
to  render  the  entire  mass  of  the  grain  capable  of  reduction. 
The  grain  may  contain  any  number  of  nuclei.  Consequently 
different  emulsions,  even  of  the  same  speed,  may  possess 
entirely  different  numbers  of  developable  grains  (per  unit 
area)  for  the  same  exposure,  and  the  relation  between  the 
number  of  developable  grains  and  the  exposure  may  vary  with 

109 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


the  latter.  Therefore,  the  only  logical  measure  of  the  latent 
image  is  the  number  of  nuclei  formed  per  unit  area;  but  the 
measure  of  the  effective  latent  image,  or  of  the  reducible 
halide  as  understood  here  must  be  the  number  of  developable 
grains.  The  only  way  the  latent  image  manifests  itself  is 
by  reduction  to  metallic  silver.  The  result  of  this  process 
may  be  studied  in  its  relation  to  the  energy  received  by  the 
emulsion,  and  this  relation  Hurter  and  Driffield  deduced  and 
expressed  in  the  form  mentioned  earlier  in  this  monograph. 
But  this  throws  no  light  on  the  questions  under  consideration. 
It  is  conceivable  that  grains  containing  more  nuclei  are  more 
susceptible  to  development,  though  this  point  is  open  to  dis- 
pute. However,  if  this  were  true,  it  would  afford  an  easy 
explanation  of  the  fact  that  more  energetic  developers  reduce 
more  silver.  Some  of  the  grains,  being  of  different  suscepti- 
bility, or  of  different  oxidation  potentials,  would  be  reduced 
by  a  developer  of  one  reduction  potential,  while  for  other 
grains  the  potential  required  would  be  higher.  Accordingly 
with  different  developers  there  would  be  a  kind  of  sorting 
process,  each  developer  reducing  what  it  could,  the  one  of  high- 
est reduction  potential  finally  reducing  the  largest  number 
of  grains. 

Under  these  conditions  the  latent  image  would  be  con- 
sidered as  never  fully  developed.  That  is,  referring  to  Fig.  40, 
for  log  Ei,  developer  I  produces  Z)ooi,  developer  II,  of  higher 
reduction  potential,  reduces  /)oon,  and.  developer  III  de- 
velops to  the  density  D coin- 
But  III  does  not  necessarily 
develop  all  the  grains;  so  it 
would  be  assumed  that  the 
limit  of  developability  should 
be  represented  by  DL,  and  the 
latent  image  curve  would  lie 
above  any  actually  obtained. 
Its  straight  line  portion  is  in- 
dicated in  the  figure  as  the 
dotted  line  L\. 


Fig.  40 


In  the  discussion  of  equation  20  in  Chapter  V,  it  was  stated 
that  p%,  the  equilibrium  value  of  the  density,  D  «> ,  tends  to 
approach  the  limit  represented  by  the  density  of  the  latent 
image  fully  developed,  depending  on  conditions.  The  latter, 
mentioned  elsewhere,  include  all  the  complex  phenomena  of 
development.  But  nothing  has  been  said  as  to  the  direction 
from  which  p  %  (Deo)  approaches  Z>L.  It  is  possible  that,  as 
the  complicating  factors  are  eliminated  from  the  development 

110 


THE  THEORY  OF  DEVELOPMENT 

process,  the  limit  Z)L  may  be  approached  from  either  direction. 
Or  it  may  be  said  that  some  developers  (perhaps  most),  de- 
velop more  density  than  that  corresponding  to  the  latent 
image,  and  others  less.  Perhaps  it  will  be  possible  to  find  an 
" ideal"  developer  which  will  reduce,  grain  for  grain,  all  of 
the  latent  image.  This  hypothesis  of  course  rests  upon  the 
assumption  that  there  is  considerable  reduction  due  to  con- 
tamination and  autocatalysis,  and  to  physical  development. 
Apparently  there  is  no  definite  proof  that  development  by 
contamination  —  i.  e.,  reduction  of  a  grain  adjacent  to  one 
rather  fully  exposed  and  undergoing  development — takes 
place1.  However,  this  might  be  possible,  provided  the 
grains  are  sufficiently  close  together,  if  it  is  assumed  that  a 
single  nucleus  makes  a  grain  developable.  That  some  false 
nuclei  (nuclei  not  formed  by  light)  are  present  and  promote 
growth  of  the  silver  deposit  is  more  than  likely,  and  that 
physical  development  takes  place  to  some  extent  can  not  be 
doubted.  It  may  therefore  be  supposed  that  the  process  of 
photographic  development  consists  in  building  on  to  a  skeletal 
framework  of  latent  image  nuclei,  rather  than  in  building  up 
to  the  complete  structure.  This  conception  would  account 
for  the  fact  that  so  little  energy  in  exposure  is  required  to  give 
visible  density  on  development,  the  very  small  quantity  of 
latent  image  being  sufficient  to  initiate  development,  which 
spreads  as  it  gathers  velocity. 

According  to  this  assumption  the  latent  image  curve  might 
lie,  say,  at  Z2,  or  still  lower,  and  under  most  curves  obtained. 
There  would  seem  to  be  considerable  indirect  evidence  in  favor 
of  this  view. 

1  This  question  is  under  investigation  in  the  Laboratory. — Ed. 


Ill 


CHAPTER  VII 

VELOCITY  or  DEVELOPMENT  (Continued) 

The   Effect   of  Soluble   Bromides  on  Velocity 

Curves  and  a  Third  Method  of  Estimating 

the  Relative  Reduction  Potential 


THE  GENERAL  EFFECT  OF  BROMIDES  ON  THE  VELOCITY  AND 
ON  THE  VELOCITY  CURVES 

If  the  concentration  of  potassium  bromide  in  a  given  de- 
veloper is  varied  and  density- time  curves  (velocity  curves) 
are  plotted  at  a  fixed  exposure  for  each  concentration,  the 
effect  of  the  bromide  after  a  sufficient  concentration  is  reached 
consists  in  a  depression  of  the  density  developed  in  a  fixed 
time,  and  in  a  marked  increase  in  the  period  of  retardation  at 
the  beginning.  Only  typical  cases  may  be  cited.  Fig.  41 
gives  the  velocity  curves  for  M/20  paraminophenol  on  Emul- 
sion 3533,  with  three  concentrations  of  bromide.  The  ob- 
served densities  are  not  given,  the  curves  being  those  put 

„ through    the    observed    points 

and  the  agreement  being  suffi- 
ciently good.  Sixteen  concen- 
trations of  bromide  were  used, 
with  the  results  given  in  Table 
31  (see  page  87).  Many  simi- 
lar experiments  were  carried 
out.  The  curves  are  for  fifteen 
minutes'  development  only, 
whereas  development  was  con- 
tinued for  thirty  minutes. 


Fig.  41 


The  result  shown  in  Fig.  41  is  often  masked  if  a  developer 
which  shows  greater  retardation  with  bromide  is  used  (as  for 
example,  hydroquinone)  or  if  development  is  stopped  too  soon. 
Consequently  published  results  on  the  effects  of  bromide  on  the 
velocity  are  somewhat  at  variance  with  each  other  and  with 
those  recorded  here.  The  present  experimental  work  indi- 
cates definitely  certain  results  which  accord  throughout  with 
the  illustrations  given,  these  being  among  the  best  and  clearest 
examples  obtainable. 

112 


THE  THEORY  OF  DEVELOPMENT 


The  curves  show  a  marked  parallelism  for  longer  times. 
This  suggests  a  depression  of  the  curve,  as  for  the  plate 
curve,  a  subject  to  be  treated  later  in  this  chapter.  The 
values  of  Dm  which  are  found  from  the  equation 
D  =Dm  (1  —  e~  Klos  t/to)  decrease  with  increasing  bromide  con- 
centration, and  the  period  of  delay  before  development  begins 
increases.  The  latter  values,  as  indicated  by  the  points  on 
the  time  axis,  were  found  by  a  special  method  briefly  described 
on  page  87.  [Use  of  D  =  Dm  (1  -  e~K  <'-«).] 

As  is  to  be  expected,  if  the  velocity  is  plotted  against  the 
time  it  is  found  that  well  beyond  the  period  of  retardation  the 

velocity  has  not  changed.  Con- 
sequently, the  effect  of  bro- 
mide on  the  velocity  consists 
entirely  of  a  change  of  velocity 
at  the  beginning  (an  increase 
in  the  retardation).  This  is 
show^n  in  the  four  curves  in 
Fig.  42,  where  the  slope  of  the 
D-t  curves  is  taken  as  the  ve- 


locity and  plotted  against  the 
corresponding  times.  The  in- 
itial period  is  roughly  indicated. 


m — 


Fig.  42 


VARIATION    OF    Z)co     WITH    BROMIDE    CONCENTRATION. 
A    THIRD    METHOD    OF    ESTIMATING    THE    RELATIVE 
REDUCTION   POTENTIAL 


The  nature  of  the  variation  of 
the  maximum  or  equilibrium  den- 
sity, D  oo  ,  with  the  bromide  con- 
centration has  been  noted.  When 
D  oo  as  determined  for  each  con- 
centration is  plotted  against  the 
logarithm  of  the  corresponding 
bromide  concentration  a  straight 
line  for  a  considerable  range  re- 
sults. Typical  cases  for  different 
emulsions  and  developers  areillus- 
strated.  Some  of  these  are  from 
the  data  for  the  determination  of 
the  density  depression,  d,  used  in 
Chapter  II,  but  not  all  of  that 
material  could  be  used  here,  as  the 
density-time  curves  were  not  al- 
ways obtained  for  a  sufficiently 
wide  range.  Fig.  43  gives  results, 

113 


77LOG.Cao       63       ae       as        92       as 


Fig.  43 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

for  the  four  developers  indicated,  on  Seed  23  emulsion  of 
May,  1917,  and  Fig.  44  gives  one  curve  for  each,  on  different 
emulsions,  as  follows : 


Fig.  44-A 


Fig.  44-B-C 


Fig.  44A     M/25  Bromhydroquinone  on  Pure  Bromide  II: 

Fig.  44B     M/20  Hydroquinone  on  Special  Emulsion  VIII; 

Fig.  44C      M/20  Dimethylparaminophenol  on  Special  Emulsion  IV; 

Fig.  45  shows  the  most  com- 
plete curve  obtained,  the  data 
being  for  M/20paraminophenol 
hydrochloride    on    Emulsion 
3533,  an  ordinary  fast  emulsion. 
Some    of    the  curves  shown 
are    better    than    the  average. 
Many    of    the    less    consistent 
Fig-  45  cases  may  be  explained  by  the 

fact  that  it  was  not  possible  to  secure  a  sufficient  number  of 
observations.  All  the  data  were  treated  as  in  the  depression 
study,  the  observations  being  least-squared  for  slope  and  in- 
tercept after  it  was  evident  that  a  straight  line  function  was 
under  consideration. 

Table  24  is  an  analysis  of  the  results  for  the  slope.  It  was 
found  that  the  slope  resembles  that  for  the  depression  curves 
and  the  values  of  m,  the  slope  of  the  d-\og  C  curves  as  given 
in  Chapter  III,  Table  4,  which  are  reoeated  here  for  compari- 
son. The  slopes  of  the  D^-log  C  curves  are  negative,  a 
fact  which  may  be  ignored  for  the  moment,  the  numerical 
values  being  of  chief  interest. 


114 


THE  THEORY  OF  DEVELOPMENT 

TABLE  24 

Comparison  of  Slopes  of  D  CD -log  C  and  d-log  C  Curves 
Numerical  Values  of  m 

SEED    23    EMULSION    OF    MAY,    1917 

Dco-logC  d-\og  C 

Bromhydroquinone m  =  .  34  m  —  .  20 

Monomethylparaminophenol .41  .28 

Toluhydroquinone .56  .52 

Paraminophenol .54  .36 

Chlorhydroquinone .40  .50 

Hydroquinone .82  .80 

Average .51  .44 

PURE    BROMIDE    EMULSION,    II 

Bromhydroquinone .48  .28 

Chlorhydroquinone .38  .38 

Paraphenylglycine .66  .70 

Average .51  .45 

SEED    23    EMULSION    OF    JUNE,    1919 

Ferrous  oxalate .35  .54 

Hydroquinone .44  .98 

Paraphenylglycine .36  .87 

Average .38  .80 

SEED  30  EMULSION  OF  JULY,   1919 

Paraphenylglycine .50  .54 

Pyrogallol 54  .42 

Dimethylparaminophenol .40  .46 

Average .48  .47 

Average  for  four  emulsions .47  .54 

Mean  of  thirty  cases m  =  .  50 

The  data  summarized  in  the  table  make  it  appear  probable 
that  the  slope  of  the  Z)co-log  C  curve  is  always  the  same 
and  equal  to  the  slope  of  the  depression  curve.  Wide  varia- 
tions occur  in  relatively  few  cases;  of  thirty  determinations, 
fifteen  lie  within  twenty  per  cent  of  the  mean  and  six  more 
within  thirty  per  cent.  (It  is  difficult  to  attain  greater  accuracy 
under  the  conditions.)  m  is  therefore  accepted  as  the  funda- 
mental constant  expressing  the  rate  of  change  of  the  equi- 
librium point  with  the  logarithm  of  the  bromide  concentra- 
tion, and,  at  the  same  time,  the  rate  of  lowering  of  the  inter- 
section point  of  the  plate  curves.  The  further  bearing  of 
these  facts  and  other  evidence  from  the  table  will  be  discussed 
in  a  following  section. 

115 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHS 

A  new  relationship  for  the  maximum  density,  analogous  to 
that  for  the  density  depression,  may  now  be  formulated. 
In  Fig.  46  I  and  II  are  the  D  m  -  log  C  curves  for  the  develop- 
ers I  and  II  used  on  the  same  emulsion.  The  slope  of  each  = 
tan  (f>  =  —m(m  being  considered  positive)  =  -  0.50  (as 
found  above).  In  general 


-  logC"0),  (35) 

where  log  C"0  is  the  intercept  on 
the  log  C  axis.  If  the  Dm- 
log  C  curve  is  a  straight  line, 
as  shown,  C"0  represents  the 
concentration  of  bromide  which 
is  required  to  restrain  develop- 
ment  completely.  That  is,  if 
the  concentration  of  bromide 
Fig-  46  present  is  C"0,  this  is  just  suf- 

ficient to  prevent  development 

at  the  given  exposure.  The  lower  region  of  the  curve  is,  however, 
much  in  doubt,  as  at  very  high  concentration  of  bromide  new 
reactions  are  indicated.  Also,  the  photometric  constant 
changes  (the  silver  becomes  very  finely  divided  and  of  a  brown 
or  red  color  by  transmitted  light)  because  of  the  state  of  divi- 
sion and  perhaps  also  the  change  of  distribution  of  the  silver 
particles.  So  far  as  observed,  therefore,  the  curve  appears 
to  dip  down,  as  shown  by  the  dotted  lines.  Hence  we  are 
unable  to  determine,  without  many  observations  of  this 
region,  the  value  of  the  concentration  of  bromide  which  will 
prevent  development.  It  is  very  probable  that  for  different 
developers  the  values  of  C'0  will  stand  in  the  same  order  and  at 
about  the  same  relative  values  as  the  concentrations  required 
to  stop  development. 

Whether  or  not  this  is  true,  it  is  possible  to  compare  develop- 
ers for  the  relative  concentrations  of  bromide  at  which  the 
same  maximum  density  is  produced.  These  will  be  in  the 
same  ratio  as  the  anti-logs  of  the  intercepts  and  probably  in 
the  same  ratio  as  the  concentrations  required  for  complete 
restraint.  The  order  of  developers  classified  in  this  way  for 
relative  energy  should  be  correct  for  compounds  which  do  not 
shift  the  entire  curve  from  its  true  position.  According  to 
relations  pointed  out  in  Chapter  VI,  some  developers  are  able 
to  reduce  more  silver  than  others  of  the  same  reduction  po- 
tential because  of  physical  or  chemical  factors  other  than  their 
relative  potentials.  Possibly  certain  of  these  factors  tend  to 
decrease  the  amount  of  silver  reduced.  Consequently  it  is  to 

116 


THE  THEORY  OF  DEVELOPMENT 

be  expected  that  some  developing  agents  will  not  be  in  their 
true  positions  in  a  classification  made  in  this  way,  as  is  prob- 
ably the  case  in  the  classification  made  by  the  previous  method. 
However,  the  maximum  densities  are  somewhat  more  accu- 
rately determined  here,  since  several  concentrations  of  bro- 
mide are  used  and  therefore  an  average  curve  can  be  obtained, 
and  some  of  the  errors  present  in  the  second  method  are 
eliminated. 

The  method  of  comparison  used  is  as  follows :  The  average 
value  of  m  found  is  0.50  (Table  25).  A  straight  line  of  slope 
-  m  (see  equation  35)  was  therefore  put  through  the  observed 
points  in  all  cases,  as  in  the  usual  treatment  of  such  data. 
Thus  a  series  of  parallel  D  <»  -  log  C  curves  for  a  number  of 
developers  on  each  plate  is  obtained,  as  typified  by  curves  I 
and  II  in  Fig.  46.  For  each  emulsion  a  convenient  standard 
value  of  Z>oo  is  taken  (D m  Std.  in  the  figure),  log  Ci  and  log 
C2  are  obtained,  and  from  these,  d  and  C2,  the  concentrations 
of  bromide  required  to  bring  the  developers  to  the  same 
equilibrium  density.  These  are  in  the  same  ratio  as  (C'0)i 
and  (C"0)2.  Ci  and  C2  are  the  relative  resistances  required  to 
produce  the  same  value  for  the  total  amount  of  work  done 
(in  reduction).  Again,  in  analogy  to  mechanical  measure- 
ments, the  amount  of  work  done  is  proportional  to  the  force 
at  work  only  if  all  other  conditions  are  constant.  This  is  not 
always  true  in  photographic  development,  so  that  this  method 
of  classification  is  less  reliable  than  that  previously  described. 

Having  obtained  the  values  of  the  bromide  concentrations 
which  correspond  to  the  standard  maximum  density,  the 
developer  for  which  the  most  consistent  data  were  obtained 
was  chosen  as  the  standard  for  each  emulsion.  Assuming  as 
before  that  the  ratio  of  the  resistances  (bromide  concentra- 
tions) measures  the  relative  reduction  potentials,  values  of 
the  latter  for  comparison  with  previous  results  can  be  obtained 

C  C* 

by   multiplying   the   ratio  ~^- ,  that  is,  -^ ,  by  the  value  of 

Cstd.  Cz 

TT  Br  found  for  the  standard  developer  by  the  first  method. 
Or,  the  relative  reduction  potential  may  be  numerically  ex- 

Q 

pressed  as  equal  to  -^-  (IT  Br)  std 

Cstd. 

Table  25  gives  the  results  obtained  in  this  way.  C  is  the 
concentration  of  bromide  corresponding  to  the  maximum 
density  stated.  The  developers  used  as  standards  on  each 
emulsion  are  indicated,  with  the  values  of  TT  Br  as  given  in 
Chapter  III. 

117 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

TABLE  25 

Concentrations  of  Bromide  Required  to  give  the  Same  D  oo  for  Different 
Developers  on  the  Same  Emulsion 

All  values  for  m  =  0.50 


For  D  oo  Relative        TTur  as 

=  3.0  Reduction       found 

Potential    previously 

r  Cx          (       \ 

Seed  23  Emulsion  of  May,  1917  C  std- 

M/25  Bromhydroquinone .25  83  21 

M/20  Monomethylparaminophenol        .  18  60  20  — 

M/20  Toluhydroquinone.  .. 035  12*  2.2 

M/20  Paraminophenol 018  (Std.  and  =6)      6  6   - 

M/20  Hydroquinone 002  1.7  1    - 

M/20  Chlorhydroquinone 003  1*  7 

M/20  Paraphenylglycine 0016  0.5  1.6    . 

For  £>oo 

Pure  Bromide  Emulsion,  II  =2.4 

C 

M/25  Bromhydroquinone 08  (Std.  and  =21)     21  21 

M/20  Chlorhydroquinone 013  3.4*  7 

M/20  Paraphenylglycine 028  5.9  1.6 

Seed  23  Emulsion  of  June,  1919          For  D  oo 

=  3.4 

M  /20  Paraphenylglycine 06  3.7  1.6- 

M/20  Hydroquinone 016  1.0  1.0. 

M  ,/10  Ferrous  Oxalate 0014  .09  0.3 

Seed  30  Emulsion  of  July,  1919          For  D  oo 

=  3.2 

M/20  Pyrogallol 11  (Std.  =  16)  16  16 

M/20  Paraphenylglycine 002  0.9  1.6 

M/20  Dimethylparaminophenol .  .  .        .25  70*  10 

An  asterisk  is  used  to  designate  those  results  which  are 
inconsistent  with  the  determinations  by  the  first  method. 
The  numerical  values  throughout  are  of  greater  range,  but 
most  of  the  developers  are  placed  in  the  same  order  as  before. 
After  obtaining  these  results  it  was  felt  that  the  method  is  of 
some  value,  yielding  additional  information  on  the  develop- 
ment process. 

The  three  methods  used  for  estimating  the  reduction  poten- 
tial are  then  : 

1.  Measuring   the   density   depression   or   lowering  of   the 
intersection  point; 

2.  Classifying    according    to    the    equilibrium    point;    and 
velocity; 

118 


THE  THEORY  OF  DEVELOPMENT 

3.  Comparing  the  concentrations  of  bromide  at  which  the 
same  amount  of  reduction  is  accomplished,  or  the  concentra- 
tions required  to  restrain  development  completely. 

Of  these  the  first  is  most  free  from  error.  The  phenomena 
described  above,  throw  more  light  on  the  density-depression 
method,  and  are  accordingly  of  more  importance  in  that  con- 
nection than  in  giving  determinations  of  the  reduction 
potential. 

EFECT  OF  BROMIDE  ON  y  oo 

The  effect  of  bromide  on  the  contrast  has  received  consider- 
able attention  from  time  to  time,  but  many  of  the  published 
results  and  conclusions  are  erroneous.  Some  practical  aspects 
of  the  subject  are  made  clearer  in  the  discussion  of  fog  (Chapter 
VIII).  Bromide  in  any  normal  developer  may,  as  shown, 
cause  a  depression  of  density  and  cut  down  fog.  Relations 
already  indicated  obtain,  with  the  following  practical  result. 
The  contrast  obtainable  in  a  given  time  may  be  lowered  if 
sufficient  bromide  is  present,  but  upon  continued  development 
the  same  contrast  will  be  reached.  The  gamma  for  a  fixed 
time  of  development  is  never  increased  by  bromide  except  in 
so  far  as  the  increased  contrast  is  due  to  the  absence  of  fog. 
Practically,  the  printing  contrast,  yA  of  the  negative  may  be 
higher  than  when  no  bromide  is  used,  because  of  the  absence 
of  fog.  Gamma  and  the  effective  contrast  should  not  be 
confused. 

y  co  is  not  affected  by  bromide  except  in  excessively  high 
concentrations.  That  is,  on  ultimate  development  the  theo- 
retical contrast  is  independent  of  the  bromide  concentration. 
In  practice  the  maximum  effective  contrast  is  usually  (because 
of  prevention  of  fog)  increased  by  bromide  to  a  certain  extent. 
The  relations  for  y  oo  as  defined  are  more  important  theo- 
retically, and  for  a  given  developer  they  aid  in  describing  the 
character  of  an  emulsion. 

The  method  for  the  determination  of  y  oo  has  been  given  in 
Chapter  VI.  Knowing  the  values  of  a,  b,  Dao  ,  and  log  E,  y  oa 
is  obtained  from  the  equation 


I       OO 


I  7—1  7  • 

logE  —  a  k 

The  effect  for  bromide  on  the  separate  factors  is  known,  a  is 
not  changed  by  bromide.  Hence  the  value  log  E  -  a  is 
constant.  D  m  decreases  as  a  straight  line  function  of  the 
logarithm  of  the  bromide  concentration,  b  increases  negatively 
in  the  same  manner  and  at  the  same  rate.  Hence  there  should 
be  no  effect  on  y  oo  . 

119 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Making  no  assumptions  for  the  time  being,  we  may  consider 
the  data  obtained  for  y  oo  . 

The  following  tables  show  for  the  highest  bromide  concen- 
trations, a  slight  lowering  of  7  oo  which  is  probably  not  real. 
At  these  high  concentrations  the  photometric  constant  changes 
in  that  the  density  observed  is  too  low  in  its  indication  of  the 
mass  of  silver.  Hence  D  oo  is  also  too  low,  and  y  oo  accord- 
ingly falls  off  as  the  concentration  increases.  But  it  is  doubt- 
ful that  the  actual  mass  of  silver  decreases  faster  than  the 
normal  rate  even  for  as  high  bromide  concentrations  as  those 
used  here.  A  study  of  the  photometric  constant  would  be 
of  value  in  this  connection. 

TABLE  26 

D  o^  —b      (a  and  b  observed 

^00  =   1r>eT°F — A     \ D  °°  computed  from  [ 
log  E -A     [observed  D  _  T  curvej 

C  (mols  per  liter  of  M/20  dimethylpara-        M/20  paraminophenol 

potassium  bromide)  minophenol  on  on  Emulsion  3533 

Special    Emulsion  IX 

7oo  7oo 

0  1.48  1.84 

.0025  1.75 

.00354  1.80 

.005  1.75 

.0078  1.68 

.01  1.45  1.65 

.014  1.71 

.02  1.45  1.71 

.0283  1.70 

04  1.43  1.65 

.057  1.53 

08  1.47  1.53 

.114  1.59 

.16  1.38  (1.37) 

.32  1.31  Relation  fails  in  this  region 


Mean  1.43  1.68 

This  slight  downward  trend  may  be  due  entirely  to  a  change 
of  grain  size  affecting  the  density  readings  at  the  higher  con- 
centrations, as  noted  above.  In  such  a  case  all  other  measure- 
ments as  recorded  previously  would  be  affected  similarly,  of 
course,  but  this  does  not  change  the  relations.  Within  the 
limit  of  error  (ten  per  cent)  the  value  of  7  oo  is  constant. 

120 


THE  THEORY  OF  DEVELOPMENT 


Table  27  gives  data  for  Seed  23  Emulsion  of  May,  1917, 
from  material  referred  to  in  the  foregoing. 


8 

ro 

ON 

- 

ON 

ON 

CN 

T-l 

10 

10 

-o 

1 

s5 

1 

1 

*f 

CO 

CN  CN 

8 

K! 

^ 

II      II 

Q 

% 

""""* 

01 

bfl  ba 

fVl 

10 

^O 

T-H 

ro 

0 

Oo 

^ 

' 

CN 

01 

1—  1 

8 

0 
i—  i 

0 

2 

ONO 

CN 

Li 

3 

" 

oJ 

01 

~H',H* 

^ 

1 

O 

T—  1 

2 

01 
10 

> 

CN 

^ 

8 

0 

cs 

o 
oo 

OO  10 

ON  t^ 

'-'  TH 

CO 

S 

oo 

CN 

s 

a 

•o 

i 

S 

3 

% 

W 

• 

^ 

oi 

T^ 

** 

'-' 

^ 

_) 

PQ 

0] 

O 

2? 

CN   ON 

00  0 

00 

0 

3 

^ 

^ 

H 

CN 

T-H^H 

^ 

1-1 

^ 

~ 

,_, 

10 

ro 

O 

^) 

«o 

^—  i 

CO 

~~t* 

^__, 

0 

'O 

o 

t 

01 

0) 

oi 

^ 

•^ 

^ 

.0 

0 

0 

_; 

o 

-t' 

^   ^ 

t^ 

oo 

00 

<*5 

t 

-—  . 

•H 

o 

-t 

10 

t^  lO 

& 

O 

-h 

-t 

< 

> 

—  H 

03 

u 

CN 

* 

c 
^o 

"o 
c 

0) 

O 

"03 

"5, 

c 

1-* 

0 

0 

c 

c 

I 

c 
c 

C 

n 

3 
3 

0 
N 

O 

o 

C=  Bromide  Conce 

"o 

Monomethylparami 

Bromhydroquinone 

Toluhydroquinone  . 

Paraminophenol  .  .  . 

Chlorhydroquinone 

Hydroquinone  

Paraphenylglycine  . 

121 


MONOGRAPHS    ON    THE    THEORY    OF    PHOTOGRAPHY 

In  the  experiments  represented  in  Tables  26  and  27  fog  is 
negligible  where  concentrations  of  bromide  are  above  .005  to 
.01  M.  The  time  required  for  a  definite  intermediate  contrast 
increases  rapidly  as  the  higher  concentrations  are  reached. 

PROOF  THAT  THE  DENSITY  DEPRESSION  MEASURES  THE  SHIFT  OF 
THE    EQUILIBRIUM,  -  1.    6.,    d     =     (Doo)o     •-    (D  oo  )  x 

As  more  data  were  secured  and  subjected  to  more  careful 
analysis,  the  evidence  became  stronger  that  the  lowering  of  the 
maximum  density  for  a  given  concentration  of  bromide  is  the 
same  as  that  of  the  density  depression.  This  corresponds  to 
the  expression 

d    =    (#00)0    -   (Poo)x, 

where  d  is  the  density  depression  (  =  -  b)  and  (D03)0  and 
(Dco)x  are  the  maximum  densities  for  the  concentrations  (of 
bromide)  0  and  x  respectively.  Direct  experimental  verifica- 
tion of  this  relation  is  not  possible  because  of  the  errors  in- 
volved, as  may  be  seen  from  an  example,  d  for  the  concentra- 
tion x  was  found  to  be  0.40  +  .05;  (Dm)0  was  4.2  Hh  .4,  and 
(Z>oo)x,  3.9  +  .2.  The  error  in  the  latter  case  is  less,  as  the 
value  is  taken  from  a  curve  through  several  observations, 
while  the  former,  (Z>oo)0»  is  a  single  determination.  The 
value  of  (Dco)0  •  (Doo)x  is  therefore  indeterminate  and 
between  the  limits  0.9  and  -  0.3,  which  renders  the  proof  that 
d  =  (Dao)o  -  (£>co)x  impossible  by  this  means.  But  other 
evidence  is  available. 

In  discussing  the  equation  7oo    =       °°     —         it  has  been 

shown  that  7  oo  and  a  are  constants  independent  of  the  bro- 
mide concentration,  and  that  D  m  and  b  vary  at  the  same  rate 
with  bromide  concentration,  since  -b  =  d  and 

d  =w(logC  -logC0),or&  =   -m(logC  -  log  C0) 
Also,  £>oo  -iff  (log  C   -  log  C"0). 

That  is,  the  rate  of  change  of  both  b  and  D  oo  with  log  C  is 
m.  (Both  diminish  as  C  increases,  b  becoming  larger 
negatively.)  Consequently,  as  the  bromide  concentration  is 
increased  a  definite  amount,  the  change  in  b  is  the  same  as  that 
in  D  oo  .  From  the  equation 


constant  = 


.  -  —  -    =  —  —  —  , 

logE  —  a         constant 

it  is  evident  that  (D  m     -  b)  is  a  constant.     Since  both  vary, 
the  change  in     -  b  is  always  equal  to  the  diminution  in  D  m  . 

122 


THE  THEORY  OF  DEVELOPMENT 

The  change  of  b  from  C  =  0  to  C  =  X  is  the  density  depression 
and  it  is  therefore  equal  to  the  shift  of  the  density  equilibrium 
point,  or  (Dm)<>  -  (#co)x  . 

Table  24,  giving  slopes  for  both  d  —  log  C  and  D  &  —  log  C 
curves,  furnishes  indirect  evidence  in  this  same  direction. 
This  evidence  lies  in  the  fact  that  both  sets  of  data  are  derived 
from  the  same  sources,  and  that  while  there  are  accidental 
errors  in  some  of  the  individual  determinations  arising  from 
plate  curves  out  of  place,  there  is  quite  marked  parallelism 
between  the  values  in  the  two  columns.  A  variation  in  the 
rate  of  density  depression  is  accompanied  by  a  similar  change 
in  the  maximum  density  curve.  This  is  due  to  a  real  relation 
between  the  two,  as  there  is  no  factor  common  to  the  two 
methods  of  computation. 

As  pointed  out,  there  is  no  direct  experimental  verification 
of  the  fact  that  d  =  (D  &  )0  -  (D  m  )x  .  Other  cases  examined 
showed  more  concordant  results  than  expected.  From  the 
nature  of  the  errors,  the  agreement  is  considered  partly 
accidental. 

TABLE  28 

Comparison  of  Density  Depression  and  Lowering  of  Equilibrium  Density 
Seed  23  Emulsion  of  May,  1917 


M/20  Paraminophenol 

C* 
01 

d 

20 

(D00)0-(D00)x 

M/20  Chlorhydroquinone 

.02 
.04 
.07 
.10 
01 

.12 
.26 
.38 
.57 
0 

.08 
.35 
.45 
.63 
05 

M/20  Paraphenylglycine 

.02 
.04 
.08 
.16 

.32 
01 

.22 
.32 
.55 
.67 
.80 
65 

.17 
.32 
.36 
.60 

.52 
16 

M/20  Hydroquinone 

.02 
.04 
005 

.70 
.92 
10 

.35 
.92 
02 

M/20  Monomethylparaminophenol 

.01 
.02 
.04 
.08 
01 

.36 
.50 

.72 
1.12 
14 

.04 

.33 
.55 
.92 
50 

*  Mols  of  potassium  bromide  per  liter. 

.02 
.04 
.08 
.16 
.32 
.64 

.'66 

.32 
.38 
.50 
.48 

',6Q 
.90 
1.10 
.70 
1.00 
(much  too  high) 

123 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

However,  the  change  of  Deo  with  bromide,  the  constancy 
of  y  co  and  of  a,  and  the  relations  for  b  are  so  well  established 
that  no  more  direct  proof  is  needed.  The  equation : 


(£ 


is  valuable  as  a  step  in  the  theory  of  the  bromide  depression 
method,  since  it  shows  that  when  the  lowering  of  the 
intersection  point  of  the  H.  and  D.  curves  is  measured  as 
described  in  the  first  three  chapters,  in  reality  the  change  in 
the  equilibrium  is  being  measured;  and  this  means  that  the 
method  is  capable  of  a  satisfactory  chemical  interpretation. 
Further,  the  expression  is  useful  in  working  out  the  more  com- 
plete relations  for  the  effect  of  bromide  on  the  velocity  curves, 
as  is  done  below. 

EFFECT  OF  BROMIDE  ON  K 

The  constant  K  in  the  velocity  equation 
D  =  Dm     1    -  g- 


includes,  (as  it  does  in  another  form  developed  by  Sheppard 
and  Mees),  the  factors  diffusivity,  diffusion  path  surface  of 
developable  halide,  and  perhaps  other  unknown  quantities. 
But  K  does  not  include  the  same  set  of  factors  here  as  it 
does  in  the  other  velocity  equations,  though  the  general 
nature  of  these  quantities  is  as  indicated.  We  should  not 
expect  a  variation  of  bromide  concentration  to  have  any 
effect  on  K,  since  the  individual  components  are  not  supposed 
to  change.  That  K  in  the  velocity  equation  used  is  practically 
constant  was  proved  by  considerable  data.  Two  complete 
cases  are  given  in  Table  29. 

TABLE  29 
Constancy  of  K  with  Variable  Bromide  Concentration 


M/20 
dimethylpa- 

M/20 
dimethylpa- 

Mols  of 
potassium 
bromide 

M/20  parami-  raminophenol 
nophenol           on  Special        Mols  of 
hydrochloride   Emulsion  IX,   potassium 
on                Experiment       bromide 

M/20  parami-   raminophenol 
nophenol           on  Special 
hydrochloride   Emulsion  IX, 
on               Experiment 

per  liter 

Emulsion  3533 

106               per  liter 

Emulsion  3533 

106 

c 

K 

K 

C 

K 

K 

.0 

.30 

.53 

.0283 

.48 

.0025 

.42 

.04 

.51 

'  .63 

.00354 

.45 

.057 

.44 

.... 

.005 

.44 

.... 

.08 

.51 

.56 

.0078 
.01 

.51 
.37 

.44 

.114 
.16 

.44 
.47 

'.'42 

.228 

.45 

.014 

.47 

.32 

.45 

".37 

.02 

.43 

A2 

.45 

.44 

Mean 

.44 

.48 

124 


THE  THEORY  OF  DEVELOPMENT 

In  Wilsey's  equation,  D  =  Dm  (1  -e-K^~^\b),  K 
decreases  and  b  increases  with  bromide  concentration,  as 
shown  by  computations  from  the  paraminophenol  data  used 
in  Table  30.  As  stated  elsewhere,  the  maximum  density 
calculated  by  this  equation  is  often  identical  with  that  obtained 

from  the  form  D  =  Dm  (1   -  e—Klost/t°).     Differences  may 

occur  for  other  types  of  curves,  but  none  was  found  in  the 
cases  computed  here.  (For  methods  see  Chapter  V.)  Table 
30  gives  the  values  of  D  oo  and  K  obtained  by  the  two  equations 
and  of  b  in  Wilsey's  equation. 

TABLE  30 
Effect  of  Bromide  on  K 


D    =  £>« 

,  (1  -  e—  K 

log  ///0) 

D  =  Do 

>  (1  -  e—  1 

ffr-W  b) 

C 

Z)oo 

K 

D  oo 

K 

b 

0 

4.20 

.30 

4.20 

.23 

.50 

.0025 

4.00 

.42 

4.00 

.19 

.59 

.005 

3.90 

.44 

3.90 

.15 

.60 

.01 

3.50 

.37 

3.50 

.27 

.50 

.04 

3.30 

.51 

3.20 

.11 

.81 

.08 

3.00 

.51 

3.00 

.05 

1.11 

.32 

2.20 

.45 

2.20 

.03 

1.03 

WITH  BROMIDE  CONCENTRATION 

t0  in  the  velocity  equation  D  =  Dm  (1  -  g— Kiog*//0)  js 
an  empirical  constant.  When  the  D  -  t  curve  is  well  fitted  by 
the  equation,  /0  indicates  the  length  of  the  period  of  retarda- 
tion. Its  relation  to  the  bromide  concentration  is  taken  up 
here  principally  because  it  is  necessary  as  a  constant  in  an 
equation  to  be  used  later. 

tQ  is  a  straight-line  function  of  the  bromide  concentration 
and  the  relation  is 

(Ox    =  k  c  +  (Oo, 

where  (Ox  is  t0  for  the  concentration  x,  C  is  the  concentra- 
tion x,  and  (Oo  is  /0  for  zero  concentration  of  bromide.  The 
straight-line  relation  is  used  for  greater  accuracy  in  the  de- 
termination of  (Oo  below. 

/a  ,  the  time  of  appearance  for  a  fixed  exposure,  has  usually 
been  measured  visually,  but  this  procedure  involves  too  many 
indefinite  factors.  A  better  method  is  to  read  off  from  the 
D  -  t  curves  the  time  of  development  required  for  a  definite 
low  density.  A  density  of  0.2  used  in  this  way  yields  more 
reliable  information  than  visual  measurements.  The  time  of 

125 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

development  required  to  give  a  density  of  0.2  at  the  standard 
exposure  is  a  straight  line  function  of  C  (the  potassium  bro- 
mide concentration)  just  as  /0  is.  Sheppard  found  ta  visual 
to  be  proportional  to  log  C.  As  a  matter  of  fact,  this  is  an 
approximation  over  a  range  up  to  .05  normal,  but  the  complete 
relations  for  /0  and  ta  have  been  investigated  and  the  expression 
found  to  be  of  the  form  stated  above : 

(Ox   =  k'c  +  (O0. 

If  the  intercepts  on  the  time  axis  are  well  determined  for 
the  D  -  t  curves,  these  values  will  be  very  close  approximations 
to  the  true  times  of  appearance.     The  values  of  these  intercepts 
(/0  and  ta  )  can  be  found  by  fitting  the  equation 
D  =  £>co  (1  -er-K  <t-to) ) 

to  the  first  part  of  the  curve  only  and  thus  evaluating  /0. 
When  this  was  done  t0  was  proportional  to  C  and  not  to  log  C 
as_before. 

EFFECTS  OF  SOLUBLE  BROMIDES  ON  VELOCITY  CURVES  AS 
SEEN  FROM  MORE   PRECISE  DATA 

Having  investigated  the  general  effects  of  bromide  on  the 
velocity  curves  and  on  the  various  factors  appearing  in  the 
velocity  equation,  it  is  possible  to  examine  more  closely  the 
effect  on  the  curves  themselves,  and  especially  on  other 
relations  between  the  equilibrium  values  obtained  with  differ- 
ent concentrations  of  bromide.  The  possibility  that  the 
velocity  curves  might  be  considered  as  shifted  downward,  or 
depressed,  by  the  action  of  bromide  in  the  same  way  that  the 
plate  curve  is,  was  suggested  to  the  writer.  It  was  thought 
that  if  a  suitable  mathematical  analysis  of  the  data  was  made, 
additional  information  would  be  secured  concerning  the 
chemical  phenomena  involved.  Experimental  proof  of  various 
hypotheses  was  necessary,  however,  and  it  was  found  that  for 
this  purpose  complete  data  as  well  as  great  accuracy  were 
necessary.  It  was  extremely  difficult  to  meet  these  require- 
ments with  some  of  the  developers  used,  and  consequently  the 
experimental  data  were  more  limited  than  is  to  be  desired. 
Again,  however,  there  is  abundant  indirect  proof  of  the  assump- 
tions made. 

To  increase  the  accuracy  represented  by  the  data,  more 
plates  were  used  for  each  bromide  concentration,  and  develop- 
ment was  carried  out  for  longer  times  (up  to  thirty  minutes). 

All  the  quantities  which  are  functions  of  the  bromide  con- 
centration (D  oo ,  /0>  ^f  etc.,)  were  determined  from  smoothed 

126 


THE  THEORY  OF  DEVELOPMENT 

curves  through  the  various  observations.  A  relatively  large 
number  of  concentrations  was  used.  Quantities  constant  and 
independent  of  bromide  concentration  (K  and  a)  were  averaged 
from  all  the  observations.  In  this  way  a  table  of  values  was 
secured  which  contains  the  least  error  for  the  conditions. 

Table  31  contains  complete  data  for  M/20  paraminophenol. 
The  observed  values  and  those  obtained  from  smoothed  curves 
through  the  observations  are  placed  side  by  side.  The  nature 
of  the  agreement  is  thus  shown  in  detail. 


TABLE  31 
Average  Data  for  Paraminophenol  1 


c 

£>oo 

Doo 

d 

d 

K 

Too 

Too 

to 

to 

t» 

> 

a 

.d 

c-2 

CJ 

-o 

8 

*  6 

<D    O 

1 

2* 

! 

1-2 

1 

1 

aja 

§ 

E 

"0  2 

^o  * 

T3   0 

0 

§ 

Si 

1 

il 

1 

P 

OJ 

1 

ll 

D,  ^ 

i8 

£ 

co  w 

-if 

1 

O 

1" 

£  S 

1 

O 

zl 

o 

II 

UO 

as 
0.2 

III 

U  o  o 

ii 

£3 

1 

.0000 

4.20 

4.00 

.30 

1  .84 

1  .80 

(1.0) 

1  .9 

.15 

.64 

.0025 

4.00 

3.94 

.6  ' 

"  '.0  " 

.42 

1  .75 

1  .73 

1.8 

1  .95 

.15 

.67 

.00354 

4.00 

3.86 

.10 

0 

.45 

1  .80 

1.69 

2.0 

2.0 

.69 

.005 

3.90 

3.79 

.09 

.04 

.44 

1  .75 

1  .68 

1.85 

2.05 

'  '.15 

.73 

.0078 

3.60 

3.71 

.22 

.12 

.51 

1  .68 

1  .68 

2.6 

2.1 

.74 

.01 

3.50 

3.63 

.27 

.19 

.37 

1  .65 

1  .68 

.88 

2.1 

'  '.15 

.74 

.014 

3.60 

3.56 

.30 

.27 

.47 

1  .71 

1.68 

2.0 

2.2 

.79 

.02 

3.40 

3.48 

.32 

.34 

.43 

.71 

1.67 

1  .85 

2  .2 

'  '.20 

.79 

.0283 

3.40 

3.41 

.48 

.41 

.48 

.70 

1  .68 

2.5 

2.3 

.83 

.04 

3.30 

3.33 

.47 

.49 

.51 

.65 

1.67 

2.65 

2.4 

"  '.25 

.86 

.057 

3.20 

3.26 

(.30) 

.57 

.44 

.53 

1  .68 

2.3 

2.6 

.50 

.96 

.08 

3.00 

3.19 

.50 

.64 

.51 

.53 

1  .68 

4.0 

2.8 

.85 

1  .03 

.114 

3.00 

3.10 

.62 

.71 

.44 

.59 

1  .67 

3.6 

3.2 

1  .4 

1.16 

.16 

2  .802 

3.022 

(.34)3 

.79 

.47 

.37 

1  .67 

4.0 

3.7 

2.1 

1  .31 

.228 

2.50 

.45 

4.5 

3.1 

.... 

.32 

2  .20 

.45 

5  .5 

4.5 

.45 

2.00 

:::: 

.44 

6.5 

Average   Average   Average 
=   .44       =1  .68     =1  .69 

1  Maximum  fog  at  C  =0,  and  after  30  minutes'  development,  was  0.60. 
z  DOO  falls  off  (error  in  photometric  constant,  etc). 
8  Straight-line  relation  fails  at  about  C  =  0.16. 

A  number  of  relations  which  have  been  pointed  out  are 
illustrated  in  this  table.  That  D  oo  decreases  with  log  C  at  the 
rate  -  m  is  shown  by  the  agreement  between  the  second  and 
third  columns.  The  constancy  of  K  and  of  y  oo  are  shown. 
We  believe  the  results  of  the  entire  experiment,  in  which  five 
hundred  plates  were  used,  to  be  as  consistent  and  accurate 
as  it  is  possible  to  secure  under  like  conditions.  The  greatest 

127 


Fig.  47 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

error  lies  in  the  determination  of  the  constants  and  variables 
for  C  =0  (no  bromide),  but  this  has  been  minimized  by  using 
the  mean  curves  and  extrapolating  to  zero. 

The  averaged  data  thus  ob- 
tained are  more  accurate  for  any 
concentration  of  bromide  than 
the  observations  at  that  con- 
centration. By  using  these  re- 
sults the  densities  for  the  D  -  t 
curves  may  be  calculated,  and 
these,  with  the  exception  of  the 
initial  period,  where  the  velocity 
equation  does  not  apply,  give 
the  result  of  observations  on 
the  velocity  curves.  Fig.  47 

gives  the  D  —  t  curves  for  developement  up  to  fifteen  minutes 
with  several  concentrations  of  bromide.  These  were  computed 
from  the  equation  D  =  D  m  (1  -  e—K-\ogt/t0j  by  using  the 
averaged  data  from  Table  31.  These  curves  should  not  be 
considered  merely  computations,  for  beyond  the  initial  period 
they  represent  the  average  results  based  on  all  the  observa- 
tions. Many  observations  were  made  for  the  range  up  to  30 
minutes'  development,  and  in  nearly  all  cases  the  observations 
agree  with  the  curves  beyond  the  initial  stage.  The  extent 
of  the  discrepancy  between  observations  and  computed  curves 
at  the  beginning  is  indicated  for  the  concentrations  0.0  and 
0.16  M  bromide.  The  exact  nature  of  the  agreement  between 
the  observations  and  the  computed  curves  may  be  seen  by 
comparing  the  values  of  D  «> ,  K,  and  t0  as  observed  and  as 
obtained  from  smoothed  curves.  These  may  therefore  be 
considered  as  experimental  observations  of  greater  precision. 

On  examining  the  nature  of  these  curves  it  is  seen  that  they 
are  parallel  beyond  the  induction  period.  Hence,  as  previously 
indicated,  the  velocity  is  unchanged  by  bromide.  Moreover 
it  appears  that  the  curves  have  been  moved  downward.  That 
the  lowering  of  the  density  at  any  time  /  (ignoring  the  begin- 
ning) is  the  same  as  the  lowering  of  the  maximum  density,  is 
demonstrated  experimentally.  That  is,  for  D0  and  Dx  (densi- 
ties for  concentrations  0  and  x)  at  time  t, 

D0  -  Dx    =  Doo    -D«>  x. 

Additional  data  similar  to  those  in  Table  31  are  given  in  Table 
32  for  M/20  dimethylparaminophenol  on  Special  Emulsion  IX. 


128 


log  E  =  3.0 
a  =  0.28 


THE  THEORY  OF  DEVELOPMENT 

TABLE  321 

m  =  .50 


Poo 

Poo 

d2 

d 

K 

Too 

Too 

to 

'o 

> 

11 

a 

u 

o 

rt 

3 

r> 

T3 
<L> 

I- 

6  1 
o  C 

•2. 

1 

tt~l  o 

0 

•rt  U 

Tl 

O 

"S 

v"O 

"S 

3 

"8 

2'^ 

^"S 

S 

Q 

> 

3  £j 

3 

t 

ft-w 

!-• 

^ 

c 

9-C 

Qo 

n 

w 

g   0 

1 

s 

£ 

I* 

E  8 

g  w 

o 

u! 

£ 

.0 

O 

o  e 
US 

uS 

fa 

c 

loge     t0 

0 

3.90 

3.90 

.53 

1.48 

1.43 

.55 

.48 

-.73 

.01 

3.80 

3.86 

+   14 

08 

.44 

1.45 

1.45 

.41 

.49 

-.71 

.02 

3.70 

3.70 

+  ^24 

'23 

.42 

1.45 

1.45 

.53 

.51 

-.67 

.04 

3.60 

3.56 

+  .31 

.38 

.63 

1.43 

1.45 

.70 

.56 

-.58 

.08 

3.40 

3.41 

+  .54 

.54 

.56 

1.47 

1.45 

.72 

.64 

-.45 

.16 

3.40 

3.26 

+  .41 

.68 

.42 

1.38 

.45 

.90 

.80 

-.22 

.32 

3.30 

3.10 

+  .33 

.83 

(Extrapo- 

.37 

1.31 

.44 

1.10 

1.11 

+  .11 

lated) 

.64 

3.10 

2.98 

+  .35 

.28 

1.28 

1.55 

1.72 

+  .54 

Average           Average 

=  .46                =  1.45 

1  Maximum  fog  at  C  =0,  after  twenty  minutes  development,  =  0.82. 

2  d  is  low  at  high  concentrations  of  bromide,  due  to  secondary  reaction. 

The  relations  for  the  depression  of  the  curves  are  well  shown. 
The  assumptions  made,  all  of  which  are  founded  on  the  results 
of  the  experiments,  and  all  of  which  have  been  discussed,  are 
summarized  below:— 

With  variable  bromide  concentration  the  following  relations 
hold  over  a  wide  range : 

1.  a  is  constant  and  independent  of  bromide  concentration; 

2.  b  increases  negatively  with  increase  of  bromide  according 
to  the  equation. 

b  -     -  m  (log  C   -  log  C0) ; 

3.  d,  the  density  depression,    =    —  b,  and  therefore 

d    -  m  (log  C     -  log  C0); 

4.  The  course  of  the  reaction  with  time  of  development  is 
represented  by  the  equation 

D     =   Dao    (1     -  g-Klog</«.) 

for  all  concentrations  of  bromide; 

5.  When  the  equation  above  is  properly  used,  D  m  represents 
the  equilibrium  value  for  the  density; 

129 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

6.  Dm    varies   with    bromide   exactly    as    b   does.     Hence 
d   =  DOOO   -  Dm*  ; 

7.  K  is  constant  and  independent  of  the  concentration  of 
bromide; 

8.  t0    is   a  linear  function  of  the  concentration  of  bromide; 

9.  D0  -  DK  =Z)ooo  -  D  oo  x  beyond  the  initial  period. 

THE  DEPRESSION  OF  THE  VELOCITY  CURVES 

The  velocity  equations  for  a  given  developer  with  concentra- 
tions of  bromide  0  and  x  (C  =  0  and  C  =  x)  for  a  common  time 
of  development,  /,  are: 

forC  =  0  D0    =  £>oo0    (1   -  e-Klo^t/i°0)  (unbromided)  (36) 
Ac    =  £>co  x  (1  -  g-Kiog'/SO  (  bromided  )  (37) 
and  the  depression  is  the  difference  between  the  two  at  the  time 
t.     Such  a  value  of  t  must  be  chosen  that  only  the  region  where 
the  velocity  is  not  affected  by  bromide   (i.   e.,   beyond   the 
period  of  induction),  is  considered.     It  is  convenient  to  express 
equation  37  somewhat  differently.     The  general  form  of  the 
velocity  equation  is 


D   =  D 
which  may  be  written 


(1    -  g-K 


K  (log  t     -log  «„)     .  log 


(38) 


(39) 


Log 


-  D 


f 


Fig.  48 


plotted  against  log  /  is  a  straight-line  of  slope  K 


and  intercept  log  /0  on  the  log  t 
axis.  It  has  been  shown  that  K 
is  constant  for  variable  bromide 
concentration.  Hence,  two  ve- 
locity curves  of  the  same  form  as 
(39)  for  C  =  Oand  C  =  x  have  the 
same  slope  K,  and  may  be  drawn 
as  parallel  straight  lines.  Refer- 
ring to  Fig.  48,  then,  K  is  the  same 
for  both  cases — that  is,  a0  =  a  x. 
In  the  triangle  ABC,  AC  is  the 
difference  between  the  inter- 
cepts. Calling  AC,  Xr  and  AB, 
Yr, 

L 


Xr     =    log   t0         -    log  t0        =    log  -^ 


130 


THE  THEORY  OF  DEVELOPMENT 


and       Yr    =  KXr    =  K  log  y^ .  (40) 

The  equation  for  the  bromided  curve  (C   =  x)  is 

£>oo 

log——  -?—         K  log  /   --  K  log  /v  (41) 

X  X 

But  from  the  equation  40 

K  log  t0x    ==  Yr    +  K  log  /Oo  .  (42) 

Making  this  substitution  in  (41)  and  converting  to  the  ex- 
ponential, we  may  write  the  equation  for  the  curve  C  =  x  in 
the  form 

Dx  =  £>cox    (1   -  e-*i°g^o+ Yr).   (bromided)     (43) 
on  now  subtracting  (43)  from  (36)  we  get  the  depression 

•*-/  Q  •*-'X  *~*  OO    0    \  -*-  ^  o/  U  QQ  _,  \  °  / 

(44) 

which  by  algebraic  treatment  and  use  of  the  assumption,  based 
on  experimental  evidence,  that  D0  -  Dx  =  Z)  oo  0  DCQK 

reduces  to  the  expression 

D0   -  Dx     =  L>oox    (e*    ..  1).  (45) 

Also,  £>oo0     -   Z>oox       =    Z)oox      (^Yr     --    1) 

from  which      D^x     e  Yr    =£>oo0-  (46) 

Substituting  the  value  of  Yr  gives  for  the  depression,  from 
equation  45 : 

d  =  £>oo0-  £>oox    =D0  -Dx  =^oox  (e  K1°g-^  -  1)      (47) 

°0 

and  the  relation 


First  let  us  test  equations  47  and  48  by  using  them  on  the 
results  given  in  Tables  31  and  32.  Table  33  gives  the  results 
for  paraminophenol  (See  Table  31).  All  logarithms  are  to 
the  base  e. 


131 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

TABLE  33 

Depression  of  Velocity  Curves  by  Bromide.     M/20  paraminophenol  on 

Emulsion  3533 


C 

,^ 

D* 

t 

?vr       L 

>«x< 

>vr    D 

.^y-D 

d  from  D 
Table 
31       F 

0-DX  D 
from 
'ig.  47 

"-D"* 

.0025 
.00354 
.005 
.0078 
.01 
.02 
.04 
.057 

.67 
.69 

.73 
.74 
.75 
.79 
.86 
.96 

3 
3 
3 
3 
3 
3 
3 
S 

.94 
.86 
.79 
.71 
.63 
.48 
.33 
.26 

1 
1 
1 
1 

1 
1 
1 

.01 
.022 
.041 
.045 
.046 
.068 
.102 

3 
3 
3 
3 
3 
3 
3 

T, 

.98 
.94 
.95 
.88 
.80 
.72 
.67 
75 

.04 
.08 
.16 
.17 
.18 
.24 
.33 
49 

0 
0 
04 
.12 
.19 
.34 
.49 
57 

'.24 
.36 
.50 

.06 
.14 
.21 
.29 

.37 
.52 
.67 

.74 

.08 
.114 
.16 

1.03 

1.16 
1.31 

3 
3 
3 

.19 
.10 
.02 

1 

1 

.188 
'.342 

3 
3 
4 

.79 
.90 
.05 

.60 
.79 
1  .03 

.64 

.71 
.79 

.67 
.96 

.81 
.90 
1.02 

Column 
1 

No. 

3i 

4 

5 

62 

73 

8 

9 

a%: 

4.00 
0.64 

.44 

1  These  values  are  taken  from  Table  31. 

2  Computed  depression. 

8  Depression  from  mean  curve  through  observations. 

If  equations  47  and  48  hold  when  applied  to  the  data,  the 
values  in  column  5  will  always  equal  4.00  (see  equation  48) 
and  the  values  in  columns  6,  7,  8,  and  9  will  be  in  agreement 
(equation  47).  The  relations  derived  are  very  closely  ap- 
proximated. In  column  5  there  is  a  slight  drop  in  the  values 
for  the  intermediate  concentrations.  (D  m  0  -  Dm  x)  in 
column  9  is  a  little  high,  apparently  because  D  m  0  is  too  high 
(i.  e.,  the  value  4.00  as  determined  from  the  average  of  the 
observations  at  other  concentrations  should  be  about  3.90). 
Column  5  also  indicates  that  D  m  0  is  somewhat  high.  But  the 
agreement  is  fairly  satisfactory  considering  the  nature  of 
photographic  data  of  this  kind. 

Table  34  gives  similar  computations  for  M/20  dimethylpara- 
minophenol  based  on  data  given  in  Table  32. 

TABLE  34 

Depression   of    Velocity   Curves   by    Bromide.     M/20  dimethyl  paramino- 
phenol on  Special  Emulsion  IX 
log  tn   =  -  0.73 

K°o  =   0.46 

_      DXo—DXx  =  from  ob- 


.01 
.02 
.04 
.08 
.16 
.32 
.64 

-.71 
-  .67 
-.58 
-  .45 

-  .22 
+  .11 
+  .54 

.009 
.028 
L.071 
.138 
.264 
.471 
.794 

3.86 
3.70 
3.56 
3.41 
3.26 
3.10 
2.98 

3.90 
3.80 
3.82 
3.88 
4.13 
4.55 
5.33 

.04                    .04 
.10                   .13 

.34                   .25 
.49                   .47 
.64                   .86 
Does  not  hold.  t0 
is  too  high. 

.08 
.23 
.38 
.54 
.68 
for  these  cases 

3.90 

132 


THE  THEORY  OF  DEVELOPMENT 

The  agreement  is  satisfactory,  but  it  is  seen  that  in  both 
cases  the  relations  fail  at  concentrations  of  bromide  greater 
than  0.16  M.  Indeed,  as  indicated  elsewhere,  the  fact  that 
the  various  "laws"  seem  to  break  down  in  this  region  may  be 
because  of  our  inability  to  determine  the  mass  of  silver  by  the 
measurement  of  density,  as  at  about  C  =  0.16  M.  in  both 
cases  the  deposits  begin  to  appear  brownish  by  transmitted 
light.  However,  from  other  data  it  is  suspected  that  a  reaction 
occurs  between  the  bromide  and  the  silver  halide  at  very  high 
concentrations,  or  that  the  bromide  exerts  some  physical 
influence. 

By  combining  certain  of  the  equations  derived  here  with 
others  previously  established  new  relations  may  be  shown, 
most  of  which,  however,  have  little  practical  application. 

The  general  conclusions  relative  to  this  subject  may  be 
summarized  as  follows: 

A  comparison  of  the  bromide  concentrations  at  which  two 
developers  can  produce  the  same  maximum  density  gives  a 
comparison  of  the  concentrations  theoretically  required  to 
prevent  development  at  the  given  exposure.  In  general  this 
gives  a  measure  of  the  relative  reduction  potentials  of  the  two 
developers,  but  it  will  not  serve  for  those  cases  in  which  factors 
other  than  the  reduction  potential  control  the  character  of 
development. 

The  maximum  contrast,  y  oo ,  is  unchanged  by  bromide. 

The  depression  of  density,  or  lowering  of  the  intersection 
point,  d,  has  been  shown  to  be  equal  to  the  shift  of  the  equili- 
brium, or 

d      =    D  000  —    D  COX- 

The  velocity  constant  K  is  not  affected  by  bromide. 

t0  and  ta  ,  the  retardation  time  and  time  of  appearance  re- 
spectively, are  linear  functions  of  the  bromide  concentration. 

The  only  effect  of  bromide  on  the  velocity  of  development  is 
a  change  during  the  period  of  induction.  After  this  stage  the 
velocity  is  independent  of  the  bromide  concentration. 

The  effect  of  bromide  on  the  velocity  curves  consists  in  a 
downward  displacement  beyond  the  initial  period.  This  dis- 
placement is  equal  to  the  normal  density  depression  d,  as 
indicated  by  equation  47  above. 


133 


CHAPTER  VIII 

The  Fogging  Power  of  Developers  and  the 
Distribution  of  Fog  over  the  Image 

THE  NATURE  OF  FOG 

Though  important  from  theoretical  and  practical  stand- 
points, the  subject  of  so-called  chemical  fog  has  received 
relatively  little  attention  from  photographic  investigators. 
Some  more  or  less  incomplete  microscopic  studies  have  been 
published,  but  they  are  not  of  importance  in  the  present 
discussion.  Theoretically  it  should  be  possible  to  secure  from 
the  study  of  fog  much  information  on  the  mechanism  of  the 
selective  reduction  of  the  latent  image,  the  fact  on  which  the 
entire  practical  application  of  photography  rests.  Present 
knowledge  of  the  properties  of  developing  agents  does  not 
offer  any  conclusive  evidence  as  to  which  of  these  properties 
is  the  factor  controlling  this  selective  action. 

No  attempt  has  been  made  in  the  present  instance  to  investi- 
gate the  subject  generally,  but  material  gathered  in  connection 
with  work  already  described  furnishes  much  information  on 
fog,  and  additional  experiments  have  been  carried  out  where 
necessary.  Several  series  of  experiments  performed  with 
different  developers  on  the  same  emulsion  gave  data  on  the 
relative  fogging  powers  of  developers,  and  miscellaneous 
results  throw  light  on  several  much-discussed  questions. 

The  term  fog  as  used  here  refers  to  the  deposit  resulting  from 
the  development  of  "unexposed"  silver  halide.  Inasmuch 
as  it  is  impossible  to  prepare  emulsions  which  do  not  contain 
some  grains  affected  by  light,  however  small  the  proportion 
of  such  grains  may  be,  some  of  them  may  be  finally  reduced, 
thus  contributing  to  the  result  known  as  chemical  fog.  Fur- 
thermore, it  has  been  shown  that  certain  compounds  have  the 
power  of  rendering  silver  bromide  developable,  turpentine 
being  a  notable  example.  Without  considering  the  nature 
of  this  action,  we  shall  refer  to  substances  of  this  kind  as  having 
the  power  of  nucleation — that  is,  of  forming  nuclei  in  the 
presence  of  which  reduction  and  deposition  of  silver  may 
ensue.  Aside  from  such  phenomena,  radio-active  substances 
are  present  everywhere  to  some  extent,  and  they  no  doubt 
contribute  developable  grains  to  the  aggregate.  Hence  an 
emulsion  always  contains  reducible  nuclei.  The  deposit 

134 


THE  THEORY  OF  DEVELOPMENT 

resulting  from  the  developable  grains  in  an  "unexposed" 
emulsion  (due  to  light,  radio-activity,  and  chemical  nucleation) 
is  termed  emulsion  fog. 

It  is  not  known  how  large  a  proportion  of  the  total  reduction 
of  presumably  unexposed  silver  bromide  is  due  to  emulsion 
fog.  Though  this  percentage  is  probably  relatively  small,  there 
is  at  present  no  verification  of  this.  Although  nucleation  may 
be  effected  in  different  ways,  the  resultant  grains  probably 
do  not  differ.  From  what  has  been  said  it  is  evident  that  the 
nature  of  the  developer  has  a  considerable  effect  on  the  degree 
to  which  the  development  of  these  unexposed  grains  takes 
place,  and  its  influence  on  this  may  differ  from  its  effect  on  the 
development  of  the  image  because  of  the  greater  dispersity 
and  different  arrangement  of  the  fog  grains.  Considering 
this,  it  is  not  necessary  to  account  for  all  of  the  fog  by  assuming 
that  new  grains  are  rendered  developable,  since  it  is  possible 
that  most  of  the  grains  forming  the  fog  image  possess  nuclei 
and  are  developable  before  the  developer  is  applied,  the  differ- 
ence in  the  developing  properties  of  different  reducers  account- 
ing for  the  variation  in  the  fog  density  obtained.  However, 
if  this  were  true,  and  no  other  grains  were  developed,  we  should 
probably  find  the  fogging  power  of  developers  standing  in  the 
same  order  as  certain  of  their  chemical  characteristics, 
especially  their  reduction  potentials.  This  has  not  been 
found  to  be  the  case.  Therefore  the  conclusion  is  that  in 
addition  to  grains  rendered  developable  by  the  action  of  light 
on  the  emulsion  and  those  in  the  emulsion  which  are  develop- 
able from  whatever  cause,  there  is  development  of  new  grains 
which  are  not  capable  of  reduction  except  by  some  specific 
action  of  the  reducing  solution.  This  is  termed  chemical 
fog,  and  is  believed  to  predominate. 

Chemical  fog  may  be  produced  in  several  ways  and  may 
vary  in  physical  and  chemical  structure.  Like  the  image, 
it  may  result  from  either  chemical  or  physical  development. 
If  from  chemical,  the  reducing  agent  or  its  salts  are  supposed 
to  have  the  power  of  nucleation,  in  which  case  the  grain  is 
developed  in  situ.  The  fog  may  differ  from  the  image  grain 
in  rate  of  development,  in  internal  structure,  and  in  arrange- 
ment. Oxidation  products  of  the  developer  may  form  a 
complex  with  the  spongy  silver  in  either  case,  whether  develop- 
ment is  chemical  or  physical.  Fog  developed  physically 
results  from  solution  of  the  silver  bromide  reduction,  and 
deposition  from  the  solution  on  nuclei  in  the  emulsion.  In 
this  case  the  structure  of  the  fog  image  is  usually  decidedly 
different  from  that  of  the  developed  image,  and  the  fog  lies 

135 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

partly  on  the  surface  of  the  latter.  It  is  often  so  fine-grained 
that  it  has  selective  scattering  power  for  light,  in  which  case 
it  is  differently  colored  in  reflected  and  in  transmitted  light. 
The  terms  pleochroic  and  dichroic  are  applied  to  this  kind  of 
fog.  Dichroic  fog  is  common  and  often  troublesome. 

We  cannot  distinguish,  except  in  a  very  general  and  quali- 
tative way,  between  fog  due  to  these  various  chemical  causes, 
nor  between  chemical  fog  and  emulsion  fog,  for  that  matter. 
Consequently  we  must  deal  with  the  entire  resultant  effect. 
It  would  not  be  surprising  to  find  (as  was  found)  that  the 
relations  for  fog  are  somewhat  different  from  those  for  the 
image. 

Mees  and  Piper  believed  fog  to  be  chiefly  a  matter  of 
reduction  potential.  The  latent  image  being  at  a  higher 
oxidation  potential  than  unexposed  silver  bromide,  the 
selective  reduction  of  the  latter  results  from  proper  adjustment 
of  the  reduction  potential  of  the  developer.  A  developer  of 
too  high  potential  reduces  the  unexposed  silver  bromide. 
Also,  the  reduction  potential  necessary  for  development  of 
either  exposed  or  unexposed  halide  is  lowered  by  increased 
solubility  of  the  silver  salt  in  the  developer.  Accordingly, 
solvents  of  silver  bromide  are  powerful  fogging  agents.  This 
is  illustrated  by  thiocarbamide  which,  Mees  and  Piper  state, 
so  increases  the  solubility  of  the  silver  bromide  that  a  developer 
to  which  it  is  added  reduces  the  whole  of  the  silver  halide. 
Time  is  required,  however,  for  the  thiocarbamide  to  lower  the 
resistance  sufficiently,  so  that  normal  ^development  begins 
first.  The  bromide  in  the  gelatine  emulsion  then  raises  the 
resistance  (locally)  and  prevents  the  action  of  the  thiocarba- 
mide. The  extent  to  which  the  fog  is  prevented  is  propor- 
tional to  the  amount  of  bromide  locally  liberated. 

Now,  although  the  action  of  thiocarbamide  is  accurately 
described  by  Mees  and  Piper,  there  is  one  fact  which  is  not 
explained  by  the  assumptions  made.  It  appears  that  the 
developer  can  reduce  no  more  silver  with  the  thiocarbamide 
than  without  it.  The  action  of  each  substance  seems  to  pro- 
ceed independently,  except  that,  as  stated,  the  by-product 
of  one  interferes  more  and  more  with  the  other.  But  the 
thiocarbamide  does  not  make  it  possible  for  the  developer  to 
reduce  any  more  or  different  grains  than  it  could  alone.  This 
experiments  recently  carried  out  tend  to  show. 

Consequently  the  explanation  previously  given  must  be 
modified  by  assuming  the  thiocarbamide  capable  of  nucleation, 
rather  than  able,  because  of  higher  reduction  potential,  to 
reduce  silver  grains  which  the  developer  can  not.  Further- 

136 


THE  THEORY  OF  DEVELOPMENT 

more  no  connection  can  be  shown  between  fogging  power  and 
reduction  potential,  it  being  a  notable  fact  that  many 
developers  (in  the  purest  possible  state)  of  remarkably  low 
reduction  potential  can  produce  excessive  fog  in  the  absence 
of  alkali.  It  therefore  seems  more  logical  not  to  begin  with 
the  assumption  that  fogging  propensity  is  governed  by  reduc- 
tion potential. 

There  is  little  doubt,  however,  that  increased  solubility  of 
silver  bromide  is  associated  with  greater  fog  density.  The 
production  of  nuclei,  or  the  chemical  action  resulting  in  this, 
is  doubtless  increased  by  higher  solubility — i.  e.,  greater 
concentration — in  the  same  manner  that  other  chemical 
reactions  are. 

FOGGING  POWER 

The  term  fogging  power  has  been  used  rather  freely  thus  far, 
though  no  precise  definition  of  it  has  been  given.  Mees  and 
Piper  defined  it  as 

d>   =-L 

K  ' 

where  F  is  the  "rate  at  which  the  developer  reduces  unexposed 
silver  bromide,  and  K  is  the  rate  at  which  the  image  is 
reduced."  F  is  not  actually  the  fogging  rate,  but  these 
investigators  found  that  fog  plotted  against  time  of  develop- 
ment gave  a  straight  line  through  the  same  origin  for  different 
cases,  from  which  they  concluded  the  fogging  rate  to  be 
proportional  to  the  density  at  any  time.  Accordingly  they 
used  observed  densities  (for  fog)  at  ten  minutes'  development. 
In  certain  cases  this  did  not  prove  satisfactory. 

K  is  the  constant  used  in  the  equation  D    =  D  oo  (1  -  e  ~Kt) . 

The  writer  finds  from  extensive  experiments  that  the  above 
relation  for  F  is  inaccurate.  As  shown  below,  the  fog-time 
curve  is  not  a  straight  line,  and  for  different  developers 
the  origin  may  vary  greatly.  Also,  the  velocity  equation 
D  =1)00(1  -  e  ~Kt)  is  not  sufficiently  well  followed  by  the 
development  of  the  image.  (See  Chapter  V.)  The  definition 
of  fogging  power  should  therefore  be  revised. 

It  has  been  shown  that  the  normal  development  process 
(for  the  image)  is  described  fairly  accurately  by  the  equation 

D   -=  Z>co(l    -  e-*lo^°).  (28) 

Experimental  data  show  that  the  fog-time  function  is  also  an 
exponential.  Accordingly  it  was  attempted  to  fit  the  expres- 
sion above  to  the  fog  curve,  but  without  success.  However, 

137 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


it  was  found  that  the  fogging  action  could  be  expressed  by  the 
first-order  reaction  law  with  a  correction  for  the  period  of 
delay.  This  equation,  discussed  in  Chapter  V,  has  the  form 


D   =  Dm(l    -  «-*<*-*•>). 
The  fogging  velocity  is  therefore  given  by 


(26) 


dD 

dt 


=  K 


-  D). 


The  computed  points  (black 


Equation  (26)  was  applied  to  many  experiments  and  found 
to  fit  the  data  closely.  Observations  of  fog  were  made  on  all 
plates  developed  for  the  previous  work,  the  readings  for  the 
fog  density  being  made  on  the  half  of  the  plate  which  had  not 
been  exposed. 

Fig.  49  illustrates  the  kind  of  data  secured.  The  upper 
curve  is  for  the  image.  The  computed  points  (black  dots) 
were  obtained  from  the  equation 

The  lower  curve  is  for  the  fog. 
dots)  were  derived  from 

The  developer  was  M/20  hydroquinone  (with  50  grams 
sodium  sulphite  and  50  grams  sodium  carbonate  per  liter) 
used  on  Seed  30  emulsion  with  no  bromide.  Many  developers 
used  in  the  same  wray  indicated  the  same  general  result  so  far 

as  velocity  equations  are  con- 
cerned. 

Thus  there  is  evidence  that 
development  of  the  image  and 
of  fog  do  not  follow  the  same 
law,   and    that    the   velocity 
Fig.  49  functions  are  different. 

Velocity    of    development 

Fogging  velocity 

This  is  to  be  explained  by  the  theories  outlined  above. 
If  chemical  fog  predominates,  as  is  supposed,  and  especially 
if  this  results  largely  from  physical  development  (as  is  also 
likely),  the  development  of  fog  grains  is  probably  less  restricted 
than  development  of  the  image,  where  the  grains  are  fixed  in 
place  and  have  a  definite  distribution.  In  other  words,  the 

138 


c 


dD          K 

•   (  n 

dt           t 
dD 

\LJ  <x> 

-  D}  Image 

D^tYwrr 

dt 

oo       /y;rog. 

THE  THEORY  OF  DEVELOPMENT 

production  of  fog  would  be  more  likely  to  follow  the  ordinary 
laws  for  a  chemical  reaction  not  subject  to  interference, 
namely,  the  first-order  reaction  law.  The  development  of 
fog  is  then  freed  from  one  of  the  most  complicating  factors, 
the  presence  of  gelatine. 

It  is  now  obvious  that  fogging  proceeds  to  a  definite  limit, 

or  equilibrium  value,  just  as  the  image  does;  but  some  of  the 

relations  for  equilibrium  values  previously  applied  do  not 
hold  for  fog. 

Table  35  gives  data  on  the  development  of  fog  and  of  the 
image  for  numerous  reducing  agents  on  Seed  30  emulsion. 
The  reducers  in  the  first  section  of  the  table  are  arranged 
in  order  of  reduction  potential  (see  column  10).  Values  in 
the  second  section  are  reasonable  determinations  from  velocity 
and  other  data.  Columns  2,  3,  and  4  give  values  of  D  oo  , 
K,  and  t0  for  the  fog,  computed  from  equation  26  above. 
Column  5  shows  the  fog  observed  after  10  minutes'  develop- 
ment, column  6  after  20  minutes'.  Columns  7,  8,  and  9  are 
the  image  characteristics  computed  from  equation  28  for 
comparison.  Column  11  shows  the  amount  of  fog  remaining 
to  be  developed  after  10  minutes  and  column  12  the  fogging 
velocity  after  10  minutes'  development.  It  is  evident  that 
none  of  the  characteristics  of  fog  vary  with  the  reduction 
potential  of  the  developer. 

It  is  inconsistent  to  seek  a  definition  of  fogging  power 
analogous  to  that  of  Mees  and  Piper.  K  for  the  image 
(applying  the  new  velocity  equation)  is  not  the  rate  of  develop- 
ment except  for  a  particular  set  of  conditions  which  are 
practically  unattainable.  The  velocity  of  development  for 
the  image  is 

dD       _*     (r>  D) 

^U  t 

Hence  K  is  the  velocity  only  when  t  =  1  and  at  the  same  time 
Doo  -  D  --=  1.  And  it  is  now  seen  that  F,  the  fog  at  time 
/,  is  not  simply  proportional  to  the  fogging  rate. 

Developers  wrere  then  classified  according  to  values  of  Doo 
for  the  fog  image,  or  the  maximum  or  equilibrium  value  for 
the  fog,  as  given  in  Table  36.  Here  the  values  of  7<Vand  the 
fogging  velocity  are  roughly  in  the  same  order.  (The  order 
is  correct  for  developers  of  equal  ^Fog  values  and  constant 
t0.)  Accordingly  it  may  be  said  that  the  fogging  powers  of 
two  developers  are  to  each  other  as  the  values  of  the  maximum 
fog.  This,  though  only  an  approximation,  is  a  practical 

139 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 


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M/10  ferrous  oxalate  
^-  Paraphenylenediamine(no  alkali) 
Hydroquinone  
Toluhydroquinone  
_  Paraminophenol.  .  .  .  .  / 

Chlorhydroquinone  / 

^  Paramino-ortho-cresol  
—^  Dimethylparaminophenol  
Pyrogallol  
'•n  Monomethylparaminophenol  ... 
M/25  bromhydroquinone  
Methylparamino-ortho-cresol..  .  . 
Diaminophenol  (no  alkali)  

Dichlorhydroquinone  
Dibrolnhydroquinone  
Phenylhydrazine  (no  alkali)  .... 
Paramino-meta-cresol  
Diaminophenol  -(-  alkali  

—  Pyrocatechin  
Duratol  
Edinol  

*  Later  work  on  the  Toluhyd 
All  developing  agents  are  very  dii 

r~7  u 

D 


THE  THEORY  OF  DEVELOPMENT 

classification  as  it  indicates  roughly  the  relative  amounts  of 
fog  produced  at  a  given  time.  But  a  fogging  agent  with  higher 
K  or  greater  t0  will  be  out  of  place  on  this  scale. 

In  Table  37  the  developers  are  arranged  in  order  of  fogging 
velocity  after  10  minutes.  This  seems  on  the  whole  the  best 
classification,  as  the  fog  for  a  definite  time  is  given  in  approxi- 
mately the  right  order  and  other  properties  are  in  a  more 
consistent  order,  though  no  definite  rules  may  be  established. 

The  three  experiments  marked  with  an  asterisk  are  obviously 
out  of  order.  In  the  case  of  paraminophenol  and  phenyl- 
hydrazine  this  is  due  to  the  high  value  of  t0,  the  time  at  which 
fogging  begins. 

Thus  it  is  obviously  impossible  to  attach  much  significance 
to  reduction  potential  so  far  as  fogging  tendencies  are  con- 
cerned. Two  other  possibilities  present  themselves.  Either 
the  fog  is  due  to  substances  other  than  the  developer,  or  the 
developers  must  be  assumed  to  have  the  power  of  nucleation 
or  the  ability  in  some  way  to  develop  the  unexposed  grains, 
and  in  a  manner  not  related  to  the  reduction  potential,  but 
depending  rather  on  other  chemical  properties.  The  first  of 
these  assumptions  is  untenable  unless  the  second  is  true. 
It  can  be  shown  that  small  quantities  of  foreign  substances 
produce  great  changes  in  the  fogging  power.  But  the  effect 
of  bromide  on  fog  is  such  as  to  make  it  quite  certain  that  these 
foreign  substances  are  of  low  reduction  potential.  This  may 
be  due  to  their  low  concentration,  but  the  maximum  fog 
values  should  be  influenced  in  the  same  way.  And  we  are 
again  confronted  by  the  evidence  that  fog  cannot  be  accounted 
for  by  reduction  potential.  A  number  of  the  developing 
agents  in  the  above  list  were  very  pure,  so  that  any  foreign 
substances  present  must  have  been  in  exceedingly  low 
concentration. 

If  we  accept  the  explanation  that  the  developers  have  other 
(and  comparatively  unknown)  specific  properties  which  con- 
trol their  solvent  action  on  silver  bromide  and  their  power  to 
reduce  silver  from  it  without  the  aid  of  large  numbers  of 
nuclei  affected  by  light,  the  results  may  later  be  shown  to  be 
in  accord.  This  opens  up  new  questions  which  cannot  be 
answered  from  present  information. 

THE  DISTRIBUTION  OF  FOG  OVER  THE  IMAGE 

From  the  time  of  Hurter  and  Driffield's  first  investigations 
numerous  workers  have  assumed  that  fog  is  evenly  distributed 
over  the  image,  and  have  accordingly  subtracted  the  fog 
readings  from  density  values  for  sensitometric  strips.  More 

141 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

TABLE  36 
Classification  of  Developers  According  to  Maximum  Fog 


O>oo) 
Fog 

(£>oo) 
Image 

77  Br 

(K) 
Fog 

(K) 
Image 

F  after 
20 
minutes 

Fogging 
Velocity 
after  10 
minutes 

Paramino-metacresol 

2  60 

4  00 

(9  5) 

16 

72 

2  51 

083 

Toluhydroquinone  

*2  .45 

4.40 

2  .2 

.19 

.63 

2  .34 

066 

Hydroquinone  
Diaminophenol  -)-  alkali  
Monomethylparaminophenol.  .  . 
Pyrogallol  
Methyl  paramino-orthocresol  .  . 
Dibromhydroquinone  
Dimethylparaminophenol  
Dichlorhydroquinone  
Diaminophenol,  no  alkali  

1.50 
1.30 
1.30 
1  .30 
1.20 
1.00 
.99 
.75 
.70 
70 

3.80 
4.2 
3.60 
4.00 
4.00 
3.80 
3.20 
3.60 
3.60 
4  20 

1  .0 
(40+) 
20 
16 
23 
(8) 
10 
(11) 
(30) 
6 

.12 
.11 
.11 
.05 
.10 
.07 
.08 
.06 
.14 
11 

.95 
.60 
.58 
.57 
.60 
.80 
.61 
.53 
.55 
44 

1.32 
1.20 
.90 
.88 
1.03 
.76 
.70 
.49 
.62 
44 

.053 
.041 
.088 
.035 
.044 
.032 
.041 
.025 
.034 
(  053) 

"Paramino-orthocresol  

.65 
.65 

3.80 
3  50 

7 
1  0 

.09 
05 

.70 
03 

.57 
18 

.022 
031 

Chlorhydroquinone  

.60 
.60 

4.00 
3  80 

7 
21 

.16 
07 

.52 
66 

.55 
55 

.024 
021 

Ferrous  oxalate  
•  Pyrocatechin 

.43 
.40 

3.10 
3  60 

0.3 

.10 
15 

.55 
52 

.38 
38 

.015 
018 

Edinol  
Duratol 

.30 

fog 

3.60 

.11 

.46 

.27 

.011 

.  Paraphenylene  diamine.no  alkali 

negligible 
fog 
negligible 

2.40 
1.70 

0.4 

.34 
.34 

.05 
.05 

*See  note  on  p.  140 

TABLE  37 
Classification  of  Developers  According  to  Fogging  Velocity 


- 

Fogging 
velocity 
after  10 
minutes 

Fogging 
velocity 
after  2 
minutes 

^Br 

Monomethylparaminophenol.  . 
Paramino-metacresol  

.088 
...    .083 

.90* 
2.51 

20 

(9.5) 

Toluhydroquinone  

...    .066 

2.34 

2.2 

Hydroquinone  

...    .053 

1.32 

1 

Paraminophenol 

053 

44* 

6 

Methylparamino-orthocresol  .  . 
Diaminophenol 

...    .044 
041 

1.03 
1   20 

23 
(40) 

Dimethylparaminophenol  
Pyrogallol 

...    .041 
035 

.70 
88 

10 
16 

Diaminophenol,  no  alkali 

034 

62 

(30) 

Dibromhydroquinone 

032 

76 

(8) 

Phenylhydrazine,  no  alkali  .  .  .  . 
Dichlorhydroquinone 

...    .031 
025 

.18* 
49 

less  than    1 

(11) 

Chlorhydroquinone 

024 

55 

Paramino-orthocresol 

022 

57 

7 

Bromhydroquinone 

021 

55 

21 

Pyrocatechin 

018 

38 

Ferrous  oxalate 

015 

38 

0.3 

Edinol 

Oil 

27 

142 


THE   THEORY  OF  DEVELOPMENT 

recently  several  investigators  have  questioned  this  procedure, 
and  one  or  two  have  suggested  what  may  now  be  proved, 
that  fog  (over  the  image)  decreases  as  the  image  density 
increases.  From  the  beginning  of  the  present  investigation 
the  total  density  was  read,  and  the  fog  determined  separately. 
The  total  densities  only  were  used  in  studying  the  results, 
and  it  was  assumed  that  the  higher  densities  were  free  from 
fog.  In  certain  cases  this  led  to  results  somewhat  different 
from  those  obtained  by  other  workers,  but  the  former  are  so 
much  more  consistent  throughout  that  they  are  considered 
excellent  indirect  evidence  on  the  question  of  fog  distribution. 

Some  features  of  this  indirect  proof  are  given  below.  The 
results  always  indicate  that  there  is  much  less  fog  over  the 
high  densities  than  over  the  low  densities. 

Fig.  39  is  an  exaggerated  example  of  how  the  contrast, 
T,  decreases  with  time  beyond  a  maximum,  a  fact  which 
can  be  explained  reasonably  only  by  the  growth  of  more  fog 
over  the  low  densities. 


D-t  curves  for  image  (top)  and  for  fog. 

Fig.  50 


LOG 

Fig.  51 


Fig.  50  gives  other  evidence  that  the  high  densities  are 
relatively  free  from  fog.  The  curve  is  density  plotted  against 
time,  both  for  the  image  and  for  the  fog.  The  developer  was 
M/20  monomethylparaminophenol.  Plates  were  developed 
for  ten  and  fourteen  minutes  in  the  presence  of  impurities 
causing  excessive  fog.  The  great  increase  in  chemical  fog 
may  be  seen  from  the  fog  curve  at  the  times  mentioned.  At 
the  same  time  the  image  densities  at  log  E  =  2.4  for  the  same 

143 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

plate  lie  on  the  normal  density-time  curve  for  the  image. 
These  are  unaffected  by  the  fog. 

Fig.  51  represents  development  of  a  Seed  23  emulsion  with 
M/20  hydroquinone  at  bromide  concentrations  0,  .001,  .004, 
and  .016  M.  The  plates  are  developed  to  equal  gammas. 
The  fog  for  the  upper  curve  is  0.48  and  for  the  lower  0.02. 
Examination  of  the  curves  shows  that  the  bromide  cuts  down 
the  fog  to  a  greater  extent  than  it  does  the  image,  though 
this  could  be  shown  much  better  by  plates  more  badly  fogged. 
The  lowering  of  the  curves  is  due  to  the  normal  depression  by 
bromide,  previously  described. 

The  procedure  of  subtracting  the  fog  from  all  densities  can 
be  shown  to  be  erroneous.  If  the  fog  is  subtracted  from  the 
upper  curve  and  the  curve  for  C  =  .016  M.,  the  resultant  curve 
for  no  bromide  will  lie  below  that  for  C  =  0.016  M. — a  result 
which  would  indicate  that  the  developer  produces  greater 
image  density  with  bromide  than  without  it.  In  this  particu- 
lar instance  it  is  probable  that  there  is  practically  no  fog  over 
the  image  in  the  region  of  correct  exposure  (the  straight  line 
region).  Such  cases  occur  frequently. 

The  relation  of  fog  density  to  bromide  concentration  has 
not  been  thoroughly  investigated  owing  to  the  low  fog  densi- 
ties when  any  appreciable  concentration  of  bromide  is  used. 
In  general,  it  is  found  that  the  addition  of  a  very  small  amount 
of  bromide  greatly  reduces  the  fog — that  is,  the  absolute 
depression  of  fog  is  greater  than  that  of  the  image.  Experi- 
ments of  a  preliminary  nature  and  indirect  evidence  indicate 
that  fog  density  may  be  a  function  of  bromide  concentration 
somewhat  different  from  image  density.  Whether  or  not  this 
is  true  we  are  not  prepared  to  state. 

With  reasonable  evidence  that  high  densities  are  free  from 
fog,  and  the  well  founded  assumption  that  the  laws  for  the 
growth  of  the  image,  as  previously  described,  are  at  least 
nearly  correct,  more  definite  ideas  of  the  distribution  of  fog 
over  the  image  may  be  expressed.  Experimental  data  for  a 
developer  giving  very  bad  fog  (impure  monomethylpara- 
minophenol)  are  given  in  Fig.  52.  The  observed  points  are 
for  five  and  ten  minutes'  development.  From  complete  data 
for  the  developer  the  intersection  of  the  H.  and  D.  straight 
lines  was  found  to  be  at  log  E  =  .32  and  on  the  log  E  axis. 

The  straight  lines  for  the  image  were  drawn  from  the 
density- time  curve  for  log  E  =  1.8.  Having  subtracted  the 
fog  from  the  total  density  for  the  lowest  exposure  (log  E  =  0) , 
and  having  made  observations  with  enough  bromide  to  elim- 
inate most  of  the  fog,  it  is  possible  to  draw  fairly  correctly 

144 


THE  THEORY  OF  DEVELOPMENT 


the  toe  of  the  curve  for  the  image.  Although  this  is  not 
absolutely  correct,  the  relations  are  probably  very  closely 
approximated.  Other  evidence  strengthens  this  belief. 


LogE 

Fig.  52 


Image  Density 

Fig.  53 


TABLE  38 


Fog  Distribution 
(Impure  Monomethylparaminophenol  on  Seed  23  Emulsion) 

After  10  minutes 


LogE  = 

0 

.3 

.6 

.9 

1.2 

1.5 

1.8 

2.1 

2.4 

Total  D 

2.45 

2.30 

2.30 

2.34 

2.40 

2.52 

2.82 

3.10 

3.36 

Image 

.20 

.38 

.68 

1.14 

1.60 

2.27 

2.82 

3.10 

3.36 

Fog 

2.25 

1.92 

1.62 

1.20 

.80 

.25 

0 

0 

0 

After  5  minutes 


Total  D 

1.38 

1.28 

1.26 

1.42 

1.72 

2.16 

2.60 

Image 

.16 

.32 

.61 

1.04 

1.55 

2.07 

2.59 

Fog 

1.22 

.96 

.65 

.38 

.17 

.09 

.01 

On  subtracting  the  image  density  as  read  off  from  the  image 
curve  which  is  free  from  fog,  the  value  of  the  fog  may  be 
obtained  for  a  given  image  density.  (See  Table  38). 
Plotting  the  value  of  fog  thus  obtained  against  the  image 
density  for  both  five  and  ten  minutes'  development  gives  the 
two  curves  of  Fig.  53,  which  are  approximately  straight  lines 
over  a  range  of  image  densities.  These  curves  indicate  that 
the  fog  varies  with  the  image  density  as  follows : 

F   =  k  (Di  -  Di0). 
145 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Here  k  is  the  slope  of  the  straight  line  and  is  negative. 
F  is  the  fog  for  the  image  density  Di,  and  Di0  is  the  intercept 
on  the  horizontal  axis,  or  the  density  over  which  there  is  no 
fog.  As  seen  from  the  figures,  the  statement  that  Di0  is  the 
minimum  density  over  which  there  is  no  fog  is  not  exact 
because  of  departure  from  the  straight-line  relation  at  higher 
densities. 

Assuming  for  the  time  being  that  these  conclusions  are 
correct,  a  relation  between  fog  and  bromide  concentration 
may  be  formulated.  Each  image  density  represents  the 
formation  of  a  certain  amount  of  soluble  bromide  in  the  emul- 
sion, and  the  concentration  of  the  bromide  may  be  roughly 
estimated  as  follows:  No  matter  what  the  exact  chemical 
mechanism  of  development  may  be,  one  ion  of  bromine  is 
formed  for  each  ion  of  silver  reduced,  and  the  bromine  will  be 
present  combined  with  sodium  (if  the  alkali  is  sodium 
carbonate).  One  gram  atom  of  silver  (108  gms.)  therefore 
corresponds  to  one  gram  molecule  (103  gms.)  of  sodium 
bromide,  and  the  two  are  produced  in  equal  amounts.  Density 
is  proportional  to  silver  by  the  photometric  constant,  P. 

P  is  defined  as  f^ when  D    =  1.00.     P  has  been  found 

10U  cm.2 

to  be  0.0103.1  For  a  density  of  1.00  therefore  about  0.01 
gm.  of  sodium  bromide  is  produced  in  an  area  of  100  sq.  cm. 
of  the  emulsion.  The  emulsion  when  swollen  has  a  thickness 
of  about  0.2  mm.  (0.  02  cm.).  The  volume  of  100  sq.  cm.  is 
therefore  2  cc.,  and  the  maximum  concentration  of  sodium 

bromide  would  be  — ^—      -  .005  gm.  per   cc.,  or  5  gm.  per 

liter.  This  is  roughly  0.05  M.,  which  represents  the  concen- 
tration if  no  diffusion  takes  place.  Of  course  the  concentration 
is  lowered  by  diffusion.  But  the  concentrations  present 
may  be  estimated  as : 

For  D  =  0.5,  C  =   .025  M.  or  less; 

1.0,  .05  M.  or  less; 

1.5,  .075  M.  or  less; 

2.0,  .10  M.  or  less; 

From  Table  38  and  the  above  it  is  evident  that  for  ten 
minutes'  development  (Fig.  52)  the  concentration  of  bromide 
required  to  prevent  fog  is  less  than  0.14  M.,  and  for  five 
minutes'  development  less  than  0.10  M.  This  corresponds 
to  greater  depression  for  the  fog  than  for  the  image  and  is 
quite  in  accord  with  other  experimental  results. 

1  Sheppard,  S.  E.,  and  Mees,  C.  E.  K.,  Investigations,  1.  c.,  p.  41. 

146 


THE  THEORY  OF  DEVELOPMENT 


If  the  same  laws  held  for  the  depression  of  fog  as  for  the 
depression  of  the  image,  fog  would  be  (in  Fig.  53)  a  straight 
line  function  of  log  D  rather  than  of  D.  It  may  be  that 
diffusion  effects  account  for  the  difference,  as  the  bromide 
produced  in  the  emulsion  diffuses  out  and  the  concentration 
changes. 

It  being  impossible  to  separate  chemical  fog  and  image 
density  by  chemical  means,  no  direct  proof  of  the  above  is 
obtainable.  However,  strong  evidence  in  this  direction  is 
afforded  by  a  study  of  the  fog  caused  by  thiocarbamide. 

THE  FOGGING  ACTION  OF  THIOCARBAMIDE 

The  practical  applications  of  the  action  of  thiocarbamide 
have  been  investigated  by  Waterhouse  and  more  recently  by 
Perley,  Frary,  Frary  and  Mitchell,  and  others.  It  was  found 
in  general  that  a  hydroquinone  developer  containing  sodium 
carbonate  gives  the  clearest  reversal  with  thiocarbamide  when 
a  careful  adjustment  of  the  ingredients  of  the  developer  is 
made.  As  partial  reversal  was  sufficient  for  the  present  pur- 
pose, time  was  not  taken  to  obtain  the  maximum  effect.  The 
developer  used  was: 

Hydroquinone  M/20  .  .        5.5  gms. 

Sodium  Sulphite 50      gms. 

Sodium  Carbonate.  ...      15      gms. 

Water  to 1000      ccs. 

The  concentration  of  thiocarbamide  was  0.003  M.  As  it 
was  very  difficult  to  secure  consistent  results  for  each  determin- 
ation, eight  to  sixteen  plates  were  developed  under  similar 
conditions  and  their  densities  averaged.  Even  so  there  are 
obvious  errors.  The  times  of  development  were  such  as  to 
give  always  the  same  contrast.  The  curve  for  hydroquinone 
in  the  absence  of  thiocarbamide  was  first  determined  (lowest 
curve,  I.,  Fig.  54).  Curves  for  the  densities  due  to  the 


Fig  54 


Fig.  55 


147 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

developer  with  thiocarbamide  were  then  obtained,  using 
different  concentrations  of  bromide.  These  (Fig.  54)  show 
the  reversal  effect,  which  decreases  as  more  bromide  is  added. 
These  data  indicate,  first,  that  there  is  a  general  deposition 
of  fog  over  the  plate  (the  plate  curve  is  raised),  which  is  due 
probably  to  increased  solubility  of  the  silver  halide,  and 
general  reduction  by  physical  development.  It  is  evident  that 
the  fog  of  the  reversed  image  (as,  for  example,  the  density  at 
log  E  =  0.8)  is  depressed  more  by  bromide  than  a  density 
lying  higher  on  the  normal  image  side  of  the  curve.  If  it  is 
assumed  that  the  hydroquinone  develops  the  same  density  in 
all  cases,  a  fact  which  separate  experiments  indicate,  the 
difference  between  any  given  curve  and  the  curve  for  the 
developer  alone  may  be  taken  as  the  fog  value.  When  these 
fog  values  are  plotted  against  the  corresponding  image  densi- 
ties— i.  e.,  the  densities  for  the  developer  alone — the  series  of 
curves  in  Fig.  55,  which  bear  a  marked  resemblance  to  those 
of  Fig.  53  (obtained  by  a  different  method)  results.  The 
only  difference  between  the  two  sets  of  curves  is  that  in  Fig. 
55  the  physically  developed  fog  is  in  constant  amount  over 
the  plate,  as  indicated  by  the  horizontal  lines.  These  curves 
require  the  assumption  that  the  fog  is  of  two  kinds,  as  already 
indicated — the  fog  resulting  from  physical  development,  and 
that  causing  the  reversal  effect.  The  latter  is  due  no  doubt 
to  grains  in  the  emulsion  which  are  rendered  developable — 
that  is,  the  thiocarbamide,  like  some  other  compounds  con- 
taining sulphur,  has  the  power  of  nucleation  as  previously 
interpreted.  The  fog  produced  in  this  way  appears  to  be 
exactly  like  that  formed  in  the  experiment  with  monomethyl- 
paraminophenol  discussed  above,  and,  similarly,  becomes  less 
as  the  image  density  decreases.  The  parallelism  is  carried 
still  further  if  the  values  of  the  intercepts  on  the  horizontal 
axis  are  treated  as  in  the  former  experiment.  These  represent 
the  image  densities  (bromide  concentration  in  the  emulsion) 
required  to  prevent  the  fog.  But  here  bromide  is  in  the 
developer  also,  so  that,  as  the  bromide  in  the  developer  is 
increased,  less  is  required  in  the  emulsion.  Consequently 
the  concentrations  in  the  emulsion  and  in  the  developer  should 
be  added.  The  concentrations  present  in  the  emulsion  (see 
page  146)  are  found  as  follows:  For  the  upper  curve 
(C  =  0.001,  Fig.  54),  the  intercept  gives  about  1.2  in  density, 
which,  as  found  above,  corresponds  to  a  bromide  concentration 
somewhat  less  than  0.06  M.  Listing  all  these  intercept  values 
with  corresponding  concentrations  of  bromide  we  have : 


148 


THE  THEORY  OF  DEVELOPMENT 

Concentration  of 

Concentration  of  Di0  (Intercept)  bromide  in  emulsion 

bromide  in  developer  from  Fig.  55  corresponding  to  Di0  C  +  Cf 

=  C  =  C' 

.001    M.  1.2                       .06    M.  .06  M. 

.0035  M.  1.0                       .05    M.  .05  M. 

.01      M.  .8                       .04    M.  .05  M. 

.015    M.  .7                       .035M.  .05  M. 

.02      M.  .6                       .03    M.  .05  M. 

These  values  of  C'  (the  concentration  of  bromide  in  the 
emulsion)  represent  the  maximum,  as  diffusion  lowers  the 
concentration  to  a  certain  extent. 

C  -f-  Cf  is  approximately  constant  and  indicates  that  for 
the  conditions  a  bromide  concentration  slightly  under  0.05  M. 
is  required  to  eliminate  fog.  Experimentally  it  was  found 
necessary  to  use  0.03  M.  in  the  developer,  which  would  indicate 
that  0.01  to  0.02  M.  is  present  in  the  emulsion. 

The  consistency  of  all  the  data  obtained  on  fog,  and  espec- 
ially of  the  results  of  particular  experiments  like  the  above, 
lead  to  the  conclusion  that  fog  is  distributed  over  the  image 
in  the  manner  indicated  in  Figs.  53  and  55.  In  certain  cases 
general  deposition  may  occur,  as  with  thiocarbamide,  sodium 
sulphite  at  fogging  concentrations,  etc.,  but  this  may  be 
separated  from  the  general  result  by  the  methods  shown. 
Further,  it  is  believed  that  fogging  agents  are  alike  in  their 
action,  and  that  their  fogging  tendencies  are  due  to  their  power 
of  nucleation  rather  than  to  their  reduction  potentials,  prop- 
erties which  appear  to  bear  no  relation  to  one  another. 

Various  practical  considerations,  which,  however,  may  not 
be  discussed  here,  are  evident  from  the  above.  Since  fog  may 
be  greatly  restrained  by  the  use  of  bromide,  it  appears 
advisable  to  use  high  reduction  potential  developers  with 
sufficient  bromide  to  eliminate  fog  completely.  Fig.  51  shows 
how  the  contrast  in  the  lower  region  of  the  plate  curve  (the  toe) 
may  be  increased  if  fog  is  normally  present.  Except  in  so  far 
as  fog  elimination  is  concerned  it  is  not  possible  to  increase 
the  contrast  appreciably  by  the  use  of  soluble  bromides  under 
any  normal  conditions. 


149 


CHAPTER   IX 

Data  Bearing  on  Chemical  and  Physical 
Phenomena  Occurring  in  Development 

NOTE — No  attempt  will  be  made  here  to  deal  with 
theories  of  the  mechanism  of  development,  nor  even 
to  connect  fully  the  data  with  such  theories.  Far  too 
little  experimental  data  is  available  on  the  questions 
involved.  Such  data  as  have  been  accumulated 
are  published  for  the  purpose  of  adding  to  the 
information  concerning  the  phenomena  and  of 
illustrating  the  use  of  the  methods  herein  described. 


THE  EFFECT  OF  NEUTRAL  SALTS 

1.  Potassium  Bromide. 

Luppo-Cramer  attempted  to  explain  the  restraining  action 
of  bromide  as  a  colloid-chemical  phenomenon.  This  view 
was  controverted  by  Sheppard  on  the  basis  of  experimental 
results  similar  to  those  recorded  in  preceding  pages.  The 
normal  effect  of  bromide  as  described  is  much  more  logically 
explained  chemically,  as  has  been  done  by  Sheppard,  and  in 
this  monograph.  The  laws  governing  the  normal  action  of 
soluble  bromides  have  already  been  stated.  However,  at 
high  concentrations  of  bromide  new  phenomena,  which  may 
be  analyzed  by  similar  methods,  appear. 

It  has  been  found  that  the  laws  formulated  for  bromide 
action  cease  to  hold  at  concentrations  of  0.16  M.  or  there- 
abouts. The  point  at  which  this  departure  occurs  seems  to 
vary  with  the  developer,  and  appears  more  marked  the 
higher  the  reduction  potential  of  the  developer.  The  latter 
may  be  an  accidental  relation,  as  monomethylparaminophenol 
(of  high  reduction  potential)  does  not  show  the  effect  at  con- 
centrations as  high  as  0.64  M.  Pyrogallol  exhibits  it  to  a 
very  marked  degree,  and  the  following  results,  for  some  of 
which  curves  are  shown,  illustrate  what  happens  when  this 
developer  is  used  with  1.28  M.  bromide  (152  gms.  per  liter). 
It  is  remarkable  that  in  this  case  the  developing  agent  contin- 
ues to  act  in  the  presence  of  nearly  twenty-five  times  its  own 
weight  of  bromide. 

150 


THE  THEORY  OF  DEVELOPMENT 

Fig.  56  gives  the  plate  curves  obtained.  The  times  of 
development,  the  values  of  y,  and  the  fog  (F)  are  given  on 
each  curve.  Other  relations,  derived  from  the  above  plate 
curves  and  other  data,  will  be  discussed.  Fig.  57  represents 
the  density-gamma  curve  at  log  E  =  3.0,  and  Fig.  58,  the 
D  — /dev  curve  for  the  same  exposure.  Other  data  obtained 
follow : 


Fig.  56 


/ 


Fig.  57 


1.  Intersection  of  Plate  Curves.     There  is  no  common  point 
of  intersection   of  the   H.   and   D.   curves  at  concentrations 
greater  than  0.08  M.- — that  is,  the  range  of  gammas  over  which 
this    relation    holds    becomes    smaller    as    the    concentration 
increases. 

2.  Density-depression.     As  seen  from  the  above,  the  depres- 
sion cannot  be  found  by  the  usual   method.     This  may  be 
determined   for  an   intermediate  value  of    y,    however;  and 
it  is  found  to  decrease  at  concentrations  greater  than  0.08  M. 
From  the  data  it  is  seen  that  the  effect  is  due  to  the  shift  of 
log  i,  the  inertia  constantly  decreasing  as  more  bromide  is 
added. 

3.  Maximum  Contrast.     It  is  evident  that  the  maximum 
attainable  contrast  decreases  rapidly  as  the  bromide  concen- 
tration increases. 

4.  Maximum    Density.     The    maximum    densities    for    the 
higher  exposures  (log  E   =  3.0,  etc.,  see  Fig.  56)  show  normal 

151 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

relations  except  that  at  C  =  1.28  the  value  is  slightly  low. 
At  the  low  exposures  (log  E  =2.0)  the  maximum  densities 
reach  a  minimum  (plotted  against  the  concentration)  and 
then  increase  with  the  concentration.  The  density-time 
curves  for  the  high  exposure  (log  E  =  3.0)  are  of  normal 
shape,  and  are  fitted  by  the  usual  velocity  equation.  For 
the  low  exposure  (log  E  =  2.0  and  under)  the  shape  of  the 
D-t  curve  is  changed  and  after  fifteen  minutes  the  density 
increases  more  rapidly  than  for  log  E  =  3.0  for  the  same  time 
of  development. 

5.  Fog.  The  fog  on  the  unexposed  portion  of  the  plate 
shows  normal  relations  until  a  concentration  of  0.08  M.  is 
reached,  after  which  it  increases  somewhat. 

A  careful  analysis  of  these  results  shows  that  the  new  effect 
of  the  bromide  is  evident  principally  in  the  low  densities,  and 
that  it  consists  in  two  separate  phenomena.  First,  with 
pyrogallol  the  bromide  has  the  same  effect  as  a  fogging  agent 
— i.  e.,  it  renders  a  certain  amount  of  silver  bromide  develop- 
able. It  is  difficult  to  account  for  this  fact,  as  it  has  been 
observed  for  no  other  developer.  There  is  no  doubt  as  to  the 
effect,  however,  as  it  was  reproducible  and  consistent.  As 
with  normal  fog,  the  high  densities  (as  seen  from  the  normal 
character  of  the  D-t  curve)  seem  unaffected.  Whether  or 
not  this  is  true,  the  growth  of  fog  does  not  account  entirely 
for  the  nature  of  the  plate  curves  shown.  The  latter  rather 
strikingly  resemble  the  type  of  curve  obtained  for  the  develop- 
ment of  certain  papers.  It  seems  probable,  therefore,  that 
the  potassium  bromide  reacts  on  the  silver  bromide  to  form 
a  complex,  thereby  producing  in  effect  a  different  emulsion. 
Complex  ions  result  from  the  dissociation  of  the  new  salt,  and 
all  the  relations  are  changed  as  this  is  formed  in  larger  amounts. 

Experiments  with  other  developers  lead  to  similar  conclu- 
sions, though  with  them  the  results  are  slightly  different, 
especially  regarding  fog,  as  noted  above.  With  monomethyl- 
paraminophenol  no  unusual  effects  were  noted  even  with  a 
bromide  concentration  of  0.64  M.  With  bromhydroquinone, 
paraminophenol,  and  dimethylparaminophenol,  the  normal 
relations  fail  at  about  C  =  0.16  M.,  and  the  deposit  becomes 
more  and  more  colored  with  increasing  bromide  concentration. 
Wjth  the  exception  of  fog,  the  effects  in  general  are  similar  to 
those  for  pyrogallol.  It  is  therefore  believed  that  potassium 
bromide  at  high  concentrations  reacts  with  the  silver  halide 
to  form  a  complex  of  indefinite  composition,  depending  on  the 
concentration.  Aside  from  this  there  may  be  absorption 

152 


THE  THEORY  OF  DEVELOPMENT 


and  an  effect  on  the  gelatine,  but  it  does  not  appear  that 
either  accounts  for  the  result. 

2.  Potassium  Iodide. 

The  so-called  accelerating  effect  of  potassium  iodide  and 
potassium  ferrocyanide  when  added  to  certain  developers  is 
fairly  well  known.  Luppo-Cramer  has  described  similar 
results  with  other  neutral  salts.  To  some  of  these  the  methods 
described  above  have  been  applied,  though  this  was  done  more 
for  the  purpose  of  determining  the  range  over  which  the 
laws  hold  than  with  any  intent  of  investigating  the  action  of 
neutral  salts. 

Sheppard  and  Meyer  have  also  investigated  the  effect  of 
potassium  iodide.  Results  recorded  here  may  be  interpreted 
in  accordance  with  their  conclusions. 

It  has  been  found  that  potassium  iodide  shows  most  marked 
effects  with  hydroquinone  and  those  developers  for  which  the 
period  of  retardation  is  long.  With  monomethylparamin- 
ophenol  and  other  "fast"  developers  the  accelerating  effect, 
if  present,  is  masked.  M/20  dimethylparaminophenol,  a 
developer  for  which  the  bromide  effect  has  been  especially 
well  established  and  which  appears  to  be  a  normal  developer, 
was  used  in  the  experiment  described.  However,  this  devel- 
oper shows  a  short  period  of  induction,  so  that  the  experiment 
does  not  show  the  acceleration  referred  to  above.  Experi- 
ments with  other  neutral  salts  illustrate  this  acceleration, 
and  data  for  this  developer  furnish  information  on  less  obvious 
phenomena. 

There  was  little  difficulty  in  applying  the  methods.  A 
well  denned  intersection  point,  which  always  lay  on  the  log  E 
axis,  was  obtained.  The  D  - 1  curves  were  of  normal  shape 
and  the  constants  D  & ,  K,  and  t0  were  computed.  In  the 
following  table  the  data  are  summarized. 

TABLE  39 
Effect  of  Potassium  Iodide  on  M/20  Dimethylparaminophenol 


CKI 

a 

b 

D  after 
2  minutes 

Z)oo 

K 

to 

Too     = 
£>oo—  b 
logE-a 

0 
.005 
.0075 
.01 
.02 
.028 
.04 

.50 
.82 
-.40 
.20 
.44 
.70 
1.00 

0 
0 
0 
0 
0 
0 
0 

1.52 
.84 
.96 
.70 
.58 
.45 
.16 

2.80 
2.60 
2.60 
2.50 
2.00 
.90 
0.30 

.64 
.27 
.33 
.44 
.34 
.53 
.93 

.59 
.46 
.48 
.88 
.80 
.50 
.88 

1.47 

1.64 
1.44 
1.56 
.70 
.28 
.09 

153 


MONOGRAPHS  ON  THE  THEORY  OF-PHOTOGRAPHY 

Some  of  these  results  are  plotted  against  the  iodide  concen- 
trations or  the  logarithms  of  the  concentrations  for  the  sake  of 
emphasis.  Fig.  59A  shows  how  different  is  the  relation  between 
Deo  and  log  C  for  iodide  from  that  for  bromide.  (In  the  latter 

case  D  m  -  log  C  is  a  straight  line  of  slope  0.5   =  W     ^7^-) 


V 


y« 


^ 

^^-"-"'^ 

\^ 

^ 

-< 

~^~^_ 

C 

)^^~~^ 

fi 

^ 

L^-"-"^ 

+2 

r 

Fig.  59A-B 


LOGF3.0 

Fig.  60 


Fig.  59B  shows  a  still  more  striking  variation  from  bromide, 
where  y  oo  is  constant  and  independent  of  the  bromide  concen- 
tration. In  Fig.  60,  K  and  a  are  plotted  against  the  concen- 
tration. Both  are  constant  with  bromide.  Here  both  are 
variable. 

3.   Other  Neutral  Salts. 

The  character  of  the  action  of  potassium  ferrocyanide, 
potassium  oxalate,  potassium  citrate,  potassium  sulphate  and 
potassium  nitrate  was  partially  investigated.  For  this  pur- 
pose a  hydroquinone  developer  was  used,  the  basic  formula 
being: 

Hydroquinone  M/40 ....    2.75  gms. ; 

Sodium  Sulphite 3.75  gms.; 

Sodium  Carbonate 12.5    gms. ; 

Water  to 1000        cc. 

The  constants  for  the  developer  alone  wrere  determined 
first,  and  the  neutral  salts  were  then  used  in  the  concentrations 
given  below.  Table  40  gives  the  data  for  the  density  after  six 
minutes'  development  (D6f),  Dm  ,  K,  t0  (the  time  required  for 
a  density  of  0.2  [  to  =  0.2],  proportional  to  the  time  of 
appearance),  and  the  fog  for  six  and  twelve  minutes. 

154 


THE  THEORY  OF  DEVELOPMENT 

TABLE  40 

Hydroquinone  with  additions  of  neutral  salts 
Emulsion  3533 


Experi- 
ment 
No. 

Neutral  salt  used 

Concen- 
tration 

ZV 

NoBro 
£>oo 

mide 
K 

Used 

to 

1D  =  0.2 

Fe' 

Fiz' 

197 
196 
198 
200 
199 
201 
202 
203 

None 
K4  Fe  (CN)6 
K4  Fe  (CN)e 
K4  Fe  (CN)6 
K2  C2  O4.H2  O 
K3  Ce  H5  OT.  H2  O 
K2S04 
KNOs 

.'O'I'M. 

.05  M. 
.25M. 
.25  M. 

.25  M. 
.25  M. 
.25M. 

.83 
1  .17 
.91 
1  .32 
1.25 
.80 
1.36 
1.13 

3.60 
3.80 
3.60 
3.40 
3.60 
3.40 
3.60 
3.60 

.86 

.77 
.61 
.48 
.60 

.55 

:ll 

4.5 
3.6 
3.6 
2.2 
2.8 
3.7 
3.00 
3.00 

4.3 

3.5 
3.7 
2.4 

2.75 
3.7 
2  .7 
2.5 

.38 
.71 
.40 

.52 
.50 
.23 
.56 
.49 

1  .16 
1  .60 
.95 
.92 
.98 
.56 
1  .04 
1  .08 

It  is  seen  that  the  period  of  retardation  for  the  developer 
alone  is  very  great.  (/0  =  4.5  minutes,  and  the  time  of  appear- 
ance is  about  4.3  minutes.)  Each  of  the  salts  used  decreases 
the  period  of  induction,  potassium  ferrocyanide  having  the 
greatest  effect,  potassium  citrate  the  least.  The  accelerating 
effect  may  also  be  seen  from  a  comparison  of  the  densities 
produced  in  six  minutes.  Other  relations  are  obvious  from 
the  table.  It  is  notable  that  while  t0  has  been  changed,  the 
variation  of  K  is  less,  and  Z^oo  is  practically  unchanged.  In 
accordance  with  the  discussion  of  the  effect  of  bromide  on 
velocity  curves  (Chapter  VII)  this  means  that  the  neutral 
salts  change  the  relations  for  the  initial  period  only.  That 
is,  the  velocity  is  practically  unaffected  in  the  later  stages  of 
the  reaction,  though  the  velocity  change  at  the  beginning  is 
quite  marked. 

Therefore  we  are  inclined  to  attribute  the  effect  of  such 
salts,  in  distinction  from  halide  salts,  principally  to  physical 
effects  on  the  gelatine  and  possibly  to  adsorption. 


THE  EFFECT  OF  CHANGES  IN  THE  CONSTITUTION  OF 
THE  DEVELOPER 

The  developing  solution  used  was  hydroquinone  with  (1) 
variable  alkali  concentration;  (2)  variable  sulphite  concen- 
tration; (3)  variable  hydroquinone  concentration. 

The  standard  formula  for  hydroquinone  used  was 

Hydroquinone  M/20.  ..        5.5gms. 

Sodium  carbonate 50      gms. 

Sodium  sulphite 75      gms. 

Water  to 1000      cc. 

All  the  data  were  obtained  in  the  usual  manner.  The  results 
are  shown  in  Tables  41,  42  and  43,  and  the  data  for  K  and  D  m 
plotted  (for  convenience)  against  the  logarithm  of  the  variable 
concentration  are  given  in  Figs.  61,  62,  and  63.  In  each  case 

155 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

the  concentrations  of  two  of  the  constituents  of  the  developer 
are  constant,  the  other  being  varied  as  indicated. 

TABLE  41 

Hydroquinone  Developer  with  Variation  of  Sulphite  Concentration1 
Emulsion  3533.     No  bromide.     Log  E  =  2.4 


Experiment 
No. 

CNa2S023 

a 

b 

D  after 
2min. 

Dx 

K 

f 

F  after 
10  min. 

*D-.» 

Too 

155 
149 
148 
126 
150 
151 
156 

6.25 
12.5 
25 
50 
75 
100 
150 

-  .40 
-  .40 
-.34 
-  .66 
-.30 
-.24 
-  .40 

0 
0 
0 
0 
0 
0 
0 

.95 
1  .22 
.80 
1.12 
.83 
.74 
.84 

3.80 
3.60 
3.20 
3.80 
3.80 
4.50 
4.00 

.54 
.86 
1.04 
.95 
.41 
.38 
.52 

.25 
.6 
.20 
.80 
.35 
.65 
.50 

.75 
1.12 
.76 
.99 
.70 
.67 
.81 

1.0 
.80 
1.0 

1  .0 

.75 
.75 
.75 

1.35 
1.28 
1.17 
1.24 
1  .41 
1.70 
1.43 

1  Hydroquinone  M/20  (5.5  gm.  per  liter); 

Sodium  carbonate  50  gm.  per  liter; 

Sodium  sulphite  variable. 
J  Concentration  of  Na2  SOs  in  grams  per  liter. 

TABLE  42 

Hydroquinone    Developer   with   Variation   of 
Emulsion  3533.     No  bromide. 


Carbonate  Concentration1 
Log  E  =  2.4 


Experi- 
ment 
No. 

CNa2  C023 

a 

b 

D  after 
2   min. 

#00 

K 

to 

F  after 
lOmin. 

'D  ..• 

Too 

191 

?4.45 

-  .20 

0 

0 

4.00 

.70 

4.0 

3.3 

1.54 

157 

-  3  .13 

+  .04 

0 

0 

2.80 

.83 

5.3 

.26 

3.7 

1.19 

158 

6.25 

-.08 

0 

0 

4.20 

.63 

4.2 

.58 

2.75 

1.76 

159 

12.5 

-.48 

0 

.22 

3.80 

.73 

4.0 

.64 

1.90 

1.32 

160 

25 

(  -  .06) 

0 

.42 

4.40 

.72 

3.5 

.65 

1.60 

1.79 

150 

50 

-  .30 

0 

.83 

3.80 

.41 

1.35 

.70 

.90 

1.41 

161 

100 

+  .04 

0 

.76 

3.60 

.75 

3.0 

.47 

.90 

1.52 

162 

200 

+  .17 

0 

.21 

3.20 

.50 

5.3 

.21 

2.00 

1.43 

1  Hydroquinone  M/20  (5.5  gms.  per  liter). 
Sodium  sulphite  (75  gms.  per  liter). 
Sodium  carbonate  variable. 

2  Concentration  of  Na2  COs  in  grams  per  liter. 

TABLE  43 

Hydroquinone  Developer  with  Variation  of  Hydroquinone  Concentration1 
Emulsion  3533.     No  bromide.     Log  E  =  2.4 


Experi- 

C 

ment 

Hydro- 

D after 

F  after 

t 

No. 

quinone2 

a 

b 

2  min. 

#00 

K 

to 

10  min. 

D=.2 

Too 

163 

2.75 

-  .74 

0 

.26 

4.50 

.81 

4.0 

1.10J 

1.90 

1.45 

150 

5.5 

-.30 

0 

.83 

3.80 

.41 

1.35 

.70} 

.25 

1.41 

164 

11.0 

-  .15 

0 

.94 

3.80 

.57 

1  .69 

.42 

.65 

1.68 

169 

22.0 

-  .94 

0 

0.00 

4.40 

.50 

3.3 

.90 

3.15 

1.31 

Very  marked  increase  in  fog. 

Hydroquinone  variable. 

Sodium  sulphite  75  gms.  per  liter. 

Sodium  carbonate  50  gms.  per  liter. 

Concentration  of  hydroquinone  in  gms.  per  liter. 

156 


THE  THEORY  OF  DEVELOPMENT 


£ 

0            L 

P            ' 

0           I7P-M 

-0     t!8 

X 

"^-^ 

/ 

\ 

/ 

\ 

1 

- 

/ 

/ 

\ 

/ 

> 

^ 

^\ 

/ 

s 

IPG.C    i 

4           74          K 

14          134 

f 

• 

\ 

\ 

\ 

2 

>^^_^ 

\ 

y^ 

( 

^ 

\ 

/ 

\ 

/ 

^ 

y 

Variable  Sulphite 

Fig.  61 


Variable  Hydroquinone 

Fig.  63 

The   results   may   be  sum- 
marized as  follows: 

1.  With  variable  sulphite: 

a  is  approximately  constant; 

D  co   increases  with  increasing  con- 
centration; 

K   rises  to  a  maximum  and   then 
drops; 

T  oo  increases  somewhat; 


All  the  other  properties — fog,  time  of  appearance,  etc.— 
exhibit  unordered  variation,  showing  that  they  are  the  result 
of  complex  chemical  interadjustments. 

2.  As  the  concentration  of  carbonate  is  increased: 

a  decreases  to  a  minimum  and  then  increases,  indicating  somewhat 
of  a  change  in  speed,  though  there  is  irregularity; 

The  density  developed  in  two  minutes  increases  rapidly  at  first 
and  then  diminishes; 

D  oo  rises  to  a  maximum  and  falls  off; 

K  appears  to  decrease  gradually  (see  curve,  Fig.  62); 

Y  oo  shows  unordered  variation ; 


\ 

' 

' 

\ 

/ 

s 

/ 

^ 

^ 

^-^-^ 

7 

\ 

>^^ 

/ 

N 

i 

C^-3J3         625          Z5        25          SO           K»         EOOOMS^ 

Variable  Carbonate 
Fig.  62 

157 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

The  time  of  appearance  drops  to  a  minimum,  after  which  it 
increases.  This  applies  to  to  also. 

3.  The  experiments  with  hydroquinone  are  hardly  of  suffi- 
cient range  for  conclusive  evidence.  However,  it  appears 
that,  as  the  concentration  increases: 

a  increases  rapidly  (the  speed  of  the  plate  decreases)  and  then 

falls  off; 

The  density  developed  in  two  minutes  parallels  a; 
D  co  drops  to  a  minimum  and  then  increases; 
K  decreases; 
y  oo  rises  to  a  maximum,  then  decreases. 

The  time  of  appearance  and  /0  show  the  same  variation  as  a. 
We  shall  not  attempt  to  explain  these  effects  at  this  time.  It 
is  expected  that,  later,  electrochemical  data  will  be  available 
which  will  throw  light  on  the  chemical  reactions  involved, 
which  are  not  clear  at  present.  Even  so,  a  few  general 
conclusions  may  be  presented: 

1.  There  is  a  variation  of  plate  speed  with  changing  alkali 
or  hydroquinone  concentration  but  not  with  sulphite; 

2.  The  increase  of  maximum  density  with  increase  of  sul- 
phite is  probably  due  partly  to  the  formation  of  sulphite  fog 
and  partly  to  the  fact  that  the  sulphite  reacts  with  the  oxida- 
tion products  with   possible  regeneration  of  the  developing 
agent; 

3.  The    effect    of    alkali    apparently    consists    (aside    from 
chemical  considerations)  partly  in  a  physical  change  of  the 
gelatine.     The  results  may  be  accounted  for  by  a  hardening  of 
the  gelatine  at  high  concentrations  of  alkali,  which  is  in  accord 
with  work  on  gelatine. 

THE  EFFECT  OF  VARYING  THE  SULPHITE   CONCENTRATION 
WITH  MONOMETHYLPARAMINOPHENOL 

When  it  was  found  that  the  maximum  density  increased 
with  sulphite  concentration  in  the  case  of  hydroquinone,  the 
same  experiment  was  tried  with  monomethylparaminophenol 
to  determine  whether  the  relations  for  the  relative  reduction 
potentials  of  the  two  developers  as  previously  found  by  the 
maximum  density  relations  were  to  be  explained  on  this  basis. 
Three  different  sulphite  concentrations  were  used.  The 
constants  are  given  in  Table  44. 


158 


THE  THEORY  OF  DEVELOPMENT 


TABLE  44 

Variation  of  Sulphite   Concentration  with   Monomethylparaminophenol* 
Emulsion  3533.     No  bromide,     log  E  =  2.4 


Experi- 
ment 
No. 

CNa2S03 

(gms./l.) 

a 

b 

D  after 
2  minutes 

D  CO 

'  K 

t0 

153 
135 
152 

20 
50 
100 

+  .60 
0 

+  .24 

0 
0 
0 

1.60 
1.66 
1.44 

3.10 
3.60 

3.50 

.43 
.58 
.47 

.37 
.70 
67 

The  effect  is  very  slight  compared  with  that  for 
hydroquinone  for  the  same  concentration  range.  It  therefore 
appears  likely  that  certain  developers  like  hydroquinone 
give  higher  densities  than  those  corresponding  to  their  reduc- 
tion potentials  because  of  side  reactions  between  the  sulphite 
and  the  oxidation  products. 

The  above  experiments  illustrate  only  partially  the  range  of 
application  of  the  methods  which  have  been  described.  Not 
every  phase  of  this  work  is  new,  but  considerably  more  exten- 
sive use  has  been  made  of  those  features  which  appear  to  be 
most  useful  in  the  study  of  chemical  reactions  pertaining  to  the 
development  process. 

*  Monomethylparaminophenol  M/20  (9  gms.  per  liter):  Sodium  carbonate  50  gms. 
per  liter. 


159 


014  A    5  |    - 

-r  v^ 


CHAPTER  X 

General  Summary  of  the  Investigation,  with 

Some  Notes  on  Reduction  Potential  in  its 

Relation  to  Structure,  Etc. 

REDUCTION     POTENTIAL     AND     THE     EFFECT     OF     BROMIDE     ON 
DEVELOPMENT  (ASIDE  FROM  THE  EFFECT  ON  VELOCITY) 

Soluble  bromides  in  a  developer  offer  resistance  to  its 
action  in  any  or  all  of  the  following  ways: 

1.  As  products  of  a  reversible  reaction; 

2.  By  lowering  the  concentration  of  silver  ions  available  for 
reduction; 

3.  By  reaction  with  the  silver  halide  to  form  complex  ions 
from  which  the  silver  is  reduced  with  greater  difficulty. 

No  one  of  these  alone  accounts  for  the  magnitude  of  the 
observed  phenomena,  so  that  probably  all  are  involved.  The 
second  is  no  doubt  of  most  importance  at  normal  concentra- 
tions. The  third  appears  to  be  a  decided  possibility  at  higher 
concentrations  of  bromide,  though  no  direct  data  are  available.1 

In  the  absence  of  the  last  reaction  (No.  3  above),  the  rela- 
tions for  the  measurement  of  the  potential  by  means  of  the 
bromide  effect  may  be  formulated  from  theoretical  considera- 
tions, the  reduction  potential  being  some  function  of  log  [Br] 

Vl 
corresponding  to  the  equilibrium  value  of  _LAlJ_    To  obtain  this 

[Ag 
met.J 

it  would  be  necessary  to  determine  the  amount  of  bromide 
against  which  a  reducing  agent  can  just  develop.  But  this  is 
not  possible,  as  the  oxidation  products  are  unstable  and  the 
measure  of  the  energy  thus  derived  depends  on  time. 

The  amounts  of  bromide  theoretically  required  to  restrain 
development  completely  (i.  e.,  the  concentrations  against 
which  the  developer  can  just  act)  may,  however,  be  determined 
by  assuming  that  the  relations  which  obtain  for  lower  con- 
centrations of  bromide  hold  to  the  limit.  The  values  so 
obtained  give  reasonable  results.  (See  chapter  VII.) 

1  With  pyro  alone  a  reverse  action  appeared,  i.  e.,  bromide  rendered  silver  bromide  more 
susceptible  to  reduction. 

160 


THE  THEORY  OF  DEVELOPMENT 

Otherwise,  the  actual  connection  between  the  chemical 
theory  and  the  first  photographic  method  used  for  determining 
the  reduction  potential  must  be  sought  in  general  laws  and  in 
analogy.  It  is  assumed  that: 

1.  Bromide  increases  the  reaction  resistance; 

2.  The  more  powerful  the  developer  the  greater  the  con- 
centration of  bromide  required  to  produce  a  given  change  in 
the  amount  of  work  done; 

3.  The  change  in  the  total  amount  of  work  done  is  measured 
by  the  shift  of  the  equilibrium,    —  i.  e.,  by  lowering  of  the 
maximum   or  equilibrium  value  of  the  density  for  a  fixed 
exposure; 

4.  The  reduction  potentials  of  two  developers  are  therefore 
related  to  each  other  in  the  same  way  as  the  concentrations 
of  bromide  required  to  produce  the  same  change  in  the  total 
amount  of  work  done. 

No  assumption  is  made  as  to  the  form  of  the  function  relat- 
ing reduction  potential  and  bromide  concentration.  An 
arbitrary  scale  is  used,  which  can  be  converted  when  suitable 
data  are  available. 

Owing  to  the  difficulty  of  presenting  the  various  related 
phases  of  the  subject,  the  proof  that  the  first  method  (the 
density  depression  method  as  originally  suggested  by 
Sheppard)  measures  the  shift  of  the  equilibrium  was  deferred 
until  Chapter  VII.  Assuming  for  the  time  being  that  the 
connection  could  be  established,  the  action  of  bromide  on  the 
plate  curves  and  all  associated  effects  were  investigated. 

For  theoretical  purposes  only  the  straight  line  portions  of 
the  plate  curves  were  considered.  For  each  curve 

D   -=  y(log£  -log*)  (1) 

where  y  is  the  slope  of  the  straight  line  (  =  tan  a  =  —r-. —  ), 

a  log  h, 

and  log  i  is  the  intercept  on  the  log  E  axis.     Log  E  has  a 
fixed  value  throughout. 

For  a  family  of  such  curves  (i.  e.,  for  plates  developed  for 
different  times)  the  following  results  were  obtained; 

1.  When  no  bromide  is  present,  and  development  is  not 
interfered  with  by  a  solvent  of  silver  halide,  the  curves  inter- 
sect in  a  point  on  the  log  E  axis, that  is,  log  i  is  constant. 
Deviations  from  this  rule  are  due  to  errors  or  to  conditions 
already  explained ; 

2.  When  sufficient  bromide  is  present  the  curves  intersect 
in  a  point  below  the  log  E  axis. 

161 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Both  these  rules  were  first  stated  by  Hurter  and  Driffield. 
The  new  phases  of  the  present  investigation,  which  affords 
additional  proof  of  these  laws,  consist  largely  of  a  different 
method  of  interpretation  and  a  much  wider  application  of  the 
results. 

In  deducing  the  various  relations,  development  for  different 
times  under  fixed  conditions  was  considered  as  yielding  a 
family  of  straight  lines  meeting  in  a  point,  the  coordinates  of 
which  are: 

a.  abscissae,  log  E  units; 

b.  ordinates,  density  units. 

The  equation  for  any  curve  expressed  in  terms  of  the  coordi- 
nates of  the  point  of  intersection  is 

D   --    y    (logE  -  a)   +  b.  (2) 

It  is  easily  proved  that  so  long  as  the  straight  lines  meet  in  a 
point  the  relation  between  density  and  gamma  is  expressed 
by  the  equation  of  a  straight  line.  If  the  curves  do  not  meet 
in  a  point  the  D  —  y  function  is  not  a  straight  line. 

The  D  -  y  curve  is  therefore  the  criterion  used  for  a  study 
of  effects  on  the  intersection  point.  The  equation  for  this 
curve  may  be  written 

D  --  6   (y   -  A)  (3) 

or  D  =   0   y   --   64,  (4) 
and  by  comparing  (2)  and  (4)  it  is  s<  en  that 

0  =  log  E  -A  (5) 

and  b  =    -  A  6.  (6) 

From  (5)  a  =  log  E   -  0.  (7) 

In  equation  3,  0  is  the  slope  and  A  the  intercept  on  the  y 
axis.  Equations  6  and  7  show  how  the  coordinates  of  the 
point  of  intersection  may  be  found. 

The  effects  of  bromide  on  a,  b  and  0  were  determined,  and 
it  was  found  that : 

a  is  independent  of  C  (the  bromide  concentration) ; 

b  increases  negatively  as  C  increases. 

Hence  the  effect  of  bromide  is  to  lower  the  intersection  point. 
Accordingly  the  depression  of  density  maybe  interpreted  as  the 
lowering  of  this  intersection  point,  and  it  is  obvious  that  the 
depression  will  be  independent  of  y  if  a  is  constant.  This 
may  be  seen  from  the  expression  for  the  depression— 

d  =   -  b  +  b0  +  (a  -  O  y,  (8) 

162 


THE  THEORY  OF  DEVELOPMENT 

in  which  d  =  depression,  and  b  and  b0  are  the  ordinates,  a  and 
a0  the  abscissae  of  the  point  of  intersection  for  bromide  and 
for  no  bromide,  respectively.  This  equation  is  developed 
with  no  assumption  as  to  the  constancy  of  a,  but  experimental 
data  have  shown  that  a  is  constant.  Hence  a  =  a0  and 
a  •  -  a0  =  0.  Also,  b0  for  normal  development  =  0.  Therefore, 

d   =    -  b  (9) 

and  the  depression  is  measured  by  the  normal  downward 
displacement  of  the  point  of  intersection. 

From  equation  7,  6  =  log  E  -  a.  Both  log  E  and  a  are 
constant.  Hence  0  is  constant.  Therefore  for  any  given 
developer,  over  a  considerable  range  of  bromide  concentra- 
tions, the  D  -  T  curve  is  a  straight  line  of  slope  6  which  is 
constant  for  different  bromide  concentrations.  The  D  —  y 
curves  for  different  concentrations  of  bromide  are  therefore 
parallel. 

The  relation  between  the  depression  of  density  (or  lowering 
of  the  intersection  point)  and  the  logarithm  of  the  bromide 
concentration  was  found  to  be  represented  by  a  straight  line 
for  a  considerable  range.  The  equation  is 

d  =  m(\ogC  -log  C0),  (10) 

where  m  is  the  slope.  Log  C0,  the  intercept  on  the  log  C  axis, 
gives  the  concentration  of  bromide  which  is  just  sufficient  to 
cause  a  depression. 

A  number  of  experiments  with  different  developers  and 
several  emulsions  demonstrated  that  m,  the  slope,  is  approxi- 
mately constant. 


m 


d  logic  C 


This  indicates  that  the  rate  of  change  of  depression  with  log  C 
is  constant  and  independent  of  developer,  emulsion  and 
bromide  concentration. 

Therefore  different  developers  give  density  depression  curves 
of  the  same  slope  (lines  parallel  to  each  other),  but  different 
values  of  the  intercept,  log  C0.  A  comparison  of  the  intercepts 
is  thus  the  same  as  that  for  the  logarithms  of  the  concentra- 
tions of  bromide  required  to  give  the  same  depression,  or  the 
same  change  in  the  amount  of  work  done. 

If  7rBr  =  reduction  potential  (using  Br  to  indicate  de- 
termination by  the  photographic  bromide  method) 

^Br   =  kC0  (11) 

163 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

by  arbitrary  definition,  as  the  form  of  the  function  is  not 
known.  Possibly  it  may  be  "^Br.  =  k  log  C0,  or  some  other 
more  involved  form,  k  is  intermediate,  as  the  absolute 
energy  can  not  be  measured  by  present  methods.  But  by 
referring  to  a  definite  standard  developer,  relative  values  may 
be  assiged  to  7rBr  From  the  above  : 

(%•)*       _      (C0)    x     . 

' 


As  has  been  stated,  this  method  measures  the  shift  of  the 
equilibrium,  or  the  change  in  the  amount  of  work  done;  and 
from  other  considerations  it  is  shown  that  this  method  is  least 
subject  to  error.  Consequently  the  values  given  are  the  most 
reliable  data  we  have  on  the  relative  potentials. 


THE  SPEED  OF  EMULSIONS 

If  H  is  the  speed,  and  E  the  exposure  corresponding  to  a 
definite  density  in  the  region  of  correct  exposure 

H*  1  or  H=    £•  (13) 

±L  h, 

No  uniformity  exists  as  to  the  units  in  which  to  express  E  and 
as  to  the  value  of  k.  In  practice  k  has  been  assigned  the 
value  34  and  E  is  expressed  in  visual  c.  m.  s.  (of  some  definite 
source).  A  photographic  light  unit  is  needed,  and  k  should  be 
expressed  in  powers  of  10  for  greater  convenience.  Here,  k  = 
100  and  E  is  expressed  in  candle-meter-seconds  of  acetylene 
screened  to  daylight  quality. 

In  accordance  with  the  conceptions  relating  to  the  common 
intersection  point,  relations  for  the  speed  of  a  plate  are  worked 
out  in  terms  of  the  coordinates  of  the  point.  For  the  general 
case 

log  H   --  Log  k   -  a  +  ~  (14) 

From  this  it  is  evident  that  if  b  has  an  appreciable  value 
(i.  e.,  if  the  inertia  changes  with  y  ),  the  speed  depends  on  the 
contrast.  If  k  =  100  and  y  =1.0,  equation  14  becomes 

log  H   =  2   -  a  +  b.  (15) 

The  use  of  a  and  b  as  fundamental  constants  is  advocated. 
It  is  shown  that  the  inertia  point  is  not  a  fixed  characteristic 
of  an  emulsion. 

164 


THE  THEORY  OF  DEVELOPMENT 

A  few  slow  emulsions  contain  bromide,  probably  absorbed, 
and  give  a  real  value  for  b.  With  such  emulsions  the  speed 
increases  with  time  of  development  or  with  7,  as  shown  by 
equation  14. 

If  the  developer  contains  sufficient  bromide  the  effect  is  the 
same  as  if  the  bromide  were  in  the  emulsion. 

Experiments  show  that  the  speed  of  a  given  emulsion  may 
vary  widely  with  the  reducing  agent  used,  especially  when  the 
latter  is  of  the  concentration  used  in  this  investigation.  The 
variations  of  speed  observed  can  not  be  accounted  for  by  any 
of  the  better-known  chemical  properties  of  the  reducing  agent, 
reduction  potential  included. 

The  speed  may  also  be  changed  by  adjustment  of  the  con- 
centrations of  the  ingredients  of  the  developer. 

Most  of  the  phenomena  observed  are  not  of  practical  import- 
ance, though  further  study  may  reveal  methods  of  advantage. 

The  practical  application  of  speed  determination  by  the  use 
of  the  D  —  Y  curve  is  indicated.  By  this  means  a  and  b  can 
be  found,  and  equation  14  or  15  is  then  used. 

THE  VELOCITY  EQUATION,  MAXIMUM  DENSITY,   ETC. 

Five  forms  of  the  velocity  equation  have  been  considered, 
and,  on  applying  these  to  experimental  data  determined  for  a 
wider  range  of  time  than  usually  employed,  the  following  was 
found  to  describe  most  accurately  the  development  process : 

D  =  Doo  (1   -  e*i°g</<o.)  (16) 

In  the  logarithmic  form  this  is 

K  (log  /  -  log  <0)  =  log      D<°  (17) 

U  co   —  U 

The  constants  /0,  K,  and  D  oo   are  evaluated  by  plotting  log 

j: —  ^-^  against  log  /,  such  a  value  of  D  oo  being  chosen  as 
D  co  — U 

will  give  a  straight  line  when  observed  values  of  density  are 
inserted  and  plotted  against  the  corresponding  values  of  log  t. 
K  is  then  the  slope  and  log  t0  the  intercept  on  the  log  /  axis. 

This  equation  is  selected  as  giving  the  most  accurate  values 
of  D  oo  ,  the  equation  fitting  the  density- time  curve  (observed) 
accurately  beyond  the  initial  stage.  Other  equations  fitted 
the  beginning  but  showed  departures  after  a  time.  The 
equation  used  by  Hurter  and  Driffield  and  by  Sheppard  and 
Mees,  D  =  D  &  (I  -  e  ~Kt),  gives  values  of  Z)oo  too  low 

165 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

for  almost  all  developers  having  an  appreciable  period  of 
retardation.  It  fits  the  data  fairly  well  for  a  few  developers 
of  the  "rapid"  type — i.  e.,  those  with  which  the  time  of 
appearance  is  extremely  short. 

The  derivative  of  equation  17  gives  an  expression  for  the 
velocity— 

f  "  7  (Z)»    -  »• 

This  opens  up  new  questions  as  to  effects  giving  rise  to  such 
a  form,  but  these  can  not  be  answered  at  present.  From 
other  considerations,  and  from  comparison  with  a  more  com- 
plete equation  derived  theoretically  by  Sheppard,  it  is  believed 
that  the  velocity  is  not  strictly  an  inverse  function  of  the  time, 
but  that  this  relation  represents  an  approximation  to  various 
correction  factors  of  which  we  have  no  definite  knowledge. 
See  Sheppard's  equation,  Chapter  V. 

It  is  evident  that  development  can  not  be  described  by  the 
simple  first  order  velocity  equation  except  in  a  very  few  spec- 
ial cases.  Equation  16  includes  these  cases  and  is  of  much 
more  general  application. 

The  method  of  determining  the  maximum  density  curve 
for  a  given  emulsion  and  developer  is  also  described.  D  oo  is 
computed  for  different  values  of  log  E  in  the  region  free  from 
fog  (the  higher  exposures)  and  plotted  against  the  corres- 
ponding values  of  log  E.  If  the  point  of  intersection  is  known 
the  straight  line  and  upper  portion  of  the  curve  may  be  drawn. 

Equation  2  above  may  be  assumed  to  hold  to  limiting  values 
of  D  and  y.  Hence, 

Dm    =  TOO  (log  E  -  a)   +  b 
Dm    —  b 

and  r°°   =i^E^- 

This  gives  a  new  method  for  the  computation  of  the  limit  of 
contrast  to  which  a  plate  can  be  developed.  It  is  shown  that 
this  limit  can  not  be  reached  practically  because  of  fog. 

The  method  of  computing  y  oo  given  (equation  19)  yields 
much  more  consistent  and  accurate  values  than  is  possible  by 
the  method  of  Sheppard  and  Mees,1  and  it  imposes  no  re- 
strictions on  the  times  of  development  nor  on  the  values  of  y 
necessary  for  the  plates  used.  Several  weaknesses  of 
the  older  method  also  become  apparent.  The  equation 
D=D(X>(1  —  e  —  Ki)  was  used,  y  was  substituted  for  D  on  the 

1  Sheppard,  S.  E.  and  Mees,  C.  E.  K.,  Investigations,  1.  c.,  pp.  65  and  293. 

166 


THE  THEORY  OF  DEVELOPMENT 


assumption  that  y  is  proportional  to  D  (i.  e.,  the  H.  and  D. 
straight  lines  meet  in  a  point  on  the  log  E  axis).  From  two 
equations  for  ti  and  /2  where  /2  =  2ti,  the  result  was 


Tl  T2 

T  oo      =    7-       =Kt.    =    1— 


from  which 


Others  have  attempted  to  apply  this  to  all  cases,  and  the 
reasons  for  its  failure  are  now  quite  clear.  If  bromide  is 
present  in  emulsion  or  developer,  D  may  not  be  replaced  by  y 
as  was  done,  for  from  equation  3  D  =  6  (y  —A)  for  such  a  case. 
Also,  the  equation  D  =  D  «>  (1  -e~Kt)  holds  only  approximately 
for  a  very  limited  class  of  developers  when  used  without 
bromide.  Consequently  the  equation  fails  to  give  consistent 
results  when  there  is  the  slightest  departure  from  the  restric- 
tions placed  upon  it. 

There  is  definite  experimental  evidence  that  D  <x>  varies 
with  the  developer.  (See  Chapter  VI,  Tables  18,  19,  20  and 
21.)  It  is  believed  that  in  the  absenceof  side  reactions  which 
complicate  the  result,  the  maximum  density  D  oo  tends  to  be 
greater  the  higher  the  reduction  potential  of  the  developer. 
The  most  marked  exceptions  are  hydroquinone  and  its  halogen 
substitution  products.  It  is  known  that  in  the  case  of  hydro- 
quinone sodium  sulphite  and  sodium  carbonate  react  with 
the  oxidation  products,  resulting  in  a  regeneration  of  the 
reducing  agent,  possibly  according  to  this  scheme:  — 

Na2  CO3  u    , 
I.  Hydroquinone  ___  ^  Hydroqumonate; 

Na2  S03 
Na2  C03 
II.  Hydroquinonate  -          —  >    Quinonate; 

AgBr 
Na2  SO3 
Na2  CO3 

III.  Quinonate—    —  >  Hydroquinonate  +Oxyquinonate; 

Na2  SO3 

IV.  Oxyquinonate  —    —  >  Quinonate  +  Dioxyquinonate, 

Na2  C03 

as  found  by  Luther  and  Leubner.  Therefore  the  hydro- 
quinone compounds  are  capable  of  yielding  a  higher  value  for 
the  equilibrium  point  than  is  normally  the  case. 

167 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Further,  increase  of  sulphite  in  the  hydroquinone  developer 
increases  the  maximum  density  (see  Chapter  IX),  which  is 
not  the  case  with  monomethylparaminophenol. 

If  the  hydroquinones  are  excluded,  other  developers, 
classified  according  to  their  equilibrium  densities,  stand 
approximately  in  the  order  of  their  reduction  potentials. 

y  oo  depends  not  only  on  Deo  (equation  19),  but  also  on  a. 
The  latter  is  the  principal  factor  in  plate  speed  which  shows 
no  regular  variation  with  the  developer.  Hence,  in  general, 
Yoo  does  not  vary  with  the  reduction  potential  of  the  de- 
veloper, though  it  may  do  so  in  a  certain  class  of  compounds 
which  are  relatively  free  from  the  type  of  complicating  reac- 
tions already  mentioned. 

Certain  groups  of  developers  show  approximately  the  same 
retardation  time  and  the  same  value  of  K.  Within  such  a 
group  the  resistance  factor  of  the  Ohm's  law  analogy  may  be 
considered  as  constant.  Hence  the  relative  velocities  are 
measures  of  the  relative  reduction  potentials,  or  at  least 
approximate  them. 

Potential 
Velocity    =   -  — .  (20) 

Resistance 
and  if  Ri   =  R2 

Potential  =  Velocity: 

(21) 
Potential        Velocity2 

The  various  terms  of  the  resistance  (see  Chapter  I,  p.  22) 
are  included  in  the  reaction  resistance  as  indicated  by  t0  and 
K,  and  for  the  same  emulsion  other  possible  terms  of  the 
numerator  in  equation  20  are  the  same.  The  resultant  com- 
parison by  equation  21  may  not  give  a  true  numerical  result 
for  the  relative  potential,  but  it  will  be  of  the  right  order. 

An  additional  classification  of  certain  compounds  was  made 
by  this  method,  this  placing  them  in  approximately  the  same 
order  as  that  obtained  by  preceding  data. 

It  is  indicated  that  the  curve  corresponding  to  the  latent 
image  fully  developed,  with  no  reduction  of  unaffected  grains, 
may  lie  below  such  maximum  density  curves  as  may  be 
obtained  from  preceding  methods.  It  is  possible  also  that  in 
some  cases  the  latent  image  is  not  fully  developed,  but  it  is 
believed  that  in  general  the  number  of  grains  affected  by  light, 
and  considered  as  units  of  the  latent  image,  may  be  less  than 
the  number  actually  developed.  This  accounts  partially  for 

168 


THE  THEORY  OF  DEVELOPMENT 

the  small  amount  of  energy  required  to  produce  a  developable 
image.  However,  no  experimental  proof  of  this  hypothesis 
is  available. 

Considerable  data  were  secured  on  the  effect  of  soluble  bro- 
mide on  the  velocity  curves  and  on  the  maximum  density. 
If  the  bromide  concentration  is  increased  with  a  certain 
developer,  and  if  D  co  as  determined  for  each  concentration 
is  plotted  against  the  logarithm  of  the  corresponding  con- 
centration (log  C),  a  straight  line  is  obtained,  as  for  the 
density  depression.  The  equation  for  this  curve  is 

L>oo    =      -  m(\ogC  -logC'0)f  (22) 

where  —  m  is  the  slope,  log  C'0  is  the  intercept  on  the  log  C 
axis,  and  C'Q  represents  the  concentration  of  potassium  bro- 
mide theoretically  required  to  prevent  development,  or  the 
concentration  against  which  the  developer  can  just  act. 

It  is  shown  (Chapter  VII)  that  the  slope  of  theZ>oo  -log  C 
curves  is  very  nearly  the  same  as  that  for  the  d  —log  C  curves, 
except  that  the  former  is  negative. 

The  mean  of  thirty  determinations  gave  0.50  as  the  value  of 

dd  dDaz 

m  . 


d  logio  C  d  Iog10  C 

Consequently,  different  developers  yield  D  m  —  log  C  curves 
which  are  parallel,  as  for  the  depression  curves.  A  compari- 
son of  the  intercepts  is  therefore  a  measure  of  the  reduction 
potential,  assuming  that  the  latter  varies  with  the  concentra- 
tion of  bromide  against  which  the  developer  can  just  function. 
(See  Chapter  I.)  As  it  is  neither  necessary  nor  convenient  to 
compare  the  intercepts,  the  concentrations  of  bromide  at 
which  the  same  Dm  was  produced  were  compared.  (This  is 
the  same  as  comparing  the  intercepts.)  This  classification  of 
developers  gives  results  which  on  the  whole  are  comparable 
(as  to  order)  to  those  of  the  depression  method. 

It  is  shown  that  this  method  is  affected  by  the  possibility 
that  a  developer  may  give  maximum  densities  higher  than 
those  corresponding  to  its  reduction  potential,  as  in  the  case 
of  the  method  of  equilibrium  values  and  the  velocity 
comparison. 

While  Z)oo  varies  with  the  bromide  concentration,  y  oo  is 
constant  and  independent  of  C.  (See  Chapter  VII,  Tables 
26  and  27.) 

169 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

It  is  proved  (Chapter  VII,  p.  127),  that  the  density  de- 
pression measures  the  shift  of  the  equilibrium,  or  that  the 
lowering  of  the  maximum  density  is  the  same  as  the  depression 
of  the  intersection  point.  From  equation  19 

_  Dm    -  b 

[    CO  : 


log  E  —  a 

Y  oo ,  log  £,  and  a  are  constants,  and  D  <*>  and  b  vary  at  the 
same  rate  with  log  C.  Hence  D  m  -  b  =  r  oo  (log  E  —  a)  = 
constant  and  the  change  in  —  b  equals  the  change  in  D  m  for  a 
definite  increment  in  log  C.  The  change  of  -  b  from  C  =  0  to 
C  =  X  is  d  (d  =  -b)  and  is  equal  to  the  shift  of  the  density 
equilibrium  point  or  (Dm)0  -  (D ao)x.  This  may  be  written 

-b   =  d  =  (Dm)0   -  (£>oo)x  (23) 

which  means  that  the  law  of  density  depression  applies  also 
to  the  limiting  value  of  the  density.  This  relation  confirmed 
by  experiment,  places  the  first  (density  depression)  method  for 
determining  the  reduction  potentials  on  a  much  firmer  basis. 

Bromide  has  no  effect  on  K,  the  velocity  constant  (Chapter 
VII,  Table  30). 

t0  of  the  velocity  equation  and  /a  the  time  of  appearance, 
are  found  to  be  straight-line  functions  of  the  concentration 
of  bromide,  C.  The  relations  are 

(/0)x  =  ft  C  +  «0)0.  (24) 

where  (t0)x  is  the  value  at  the  concentration  x,  and  (/0)0  that 
for  C  =  0.  For  the  time  of  appearance 

(/a)x     =    k'C    +    (/a)0.  (25) 

From  complete  data  for  two  developers  used  with  many 
different  concentrations  of  bromide,  and  averaged  data  from 
smoothed  curves  for  all  the  functions  as  now  determined,  it 
may  be  shown  that  the  only  effect  of  bromide  on  the  velocity 
is  a  change  during  the  period  of  induction — i.  e.,  at  the  be- 
ginning. After  a  time  the  velocity  becomes  independent  of 
the  bromide  concentration  (See  Chapter  VII,  Figs.  42  and  47.) 

The  effect  of  bromide  on  the  curves  (a  downward  normal 
displacement  of  the  curve  beyond  the  initial  period),  which  is 
equal  to  the  depression,  d,  may  be  expressed  mathematically  as 

d=Dmo-Dmx    =  D0-DX    =  Doox  («xlo«Voo-l).    (26) 

This  signifies  that  the  density  depression  d  is  normally  not 
only  independent  of  y,  but  beyond  the  initial  stage  is  inde- 

170 


THE  THEORY  OF  DEVELOPMENT 

pendent  of  the  time  of  development  also.  Practically  this 
statement  requires  careful  analysis,  because  while  the  depres- 
sion is  in  a  sense  independent  of  y  and  of  /  even  at  the  begin- 
ning, the  value  of  D0  —  Dx  (the  actual  difference  between  the 
densities  obtained  for  C  =  0  and  C  =  X  at  a  definite  time 
during  the  early  stage)  is  not  independent  of  the  time  of 
development.  The  discrepancy  is  due  entirely  to  the  period 
of  induction,  but  it  should  be  remembered  that  the  ordinary 
useful  values  of  y  may  be  obtained  entirely  within  this 
period.  It  is  emphasized  again  that  equation  26  applies  only 
to  the  range  of  unchanged  velocity. 

The  relation  between  the  maximum  densities  corresponding 
to  C   =  0  and  to  C  =X  was  found  to  be 

D  oo  eK***J  <o0=£>co0.  (27) 

The  combination  of  equations  26  and  27  with  others  preceding 
gives  rise  to  new  and  complex  relations  which  have  not  been 
thoroughly  analyzed. 


THE   FOGGING   POWER   OF   DEVELOPERS    AND   THE    DISTRIBUTION 
OF  FOG  OVER  THE  IMAGE 

The  term  "emulsion  fog"  is  used  for  the  deposit  resulting 
from  the  development  of  grains  which  contain  nuclei  and  are 
consequently  capable  of  reduction  before  the  developer  is 
applied.  These  nuclei  may  result  from  the  action,  during 
or  after  the  making  of  the  emulsion,  of  light,  of  chemical  sub- 
stances possessing  the  power  of  rendering  the  grains  develop- 
able, or  from  radio-activity. 

It  is  supposed  that  emulsion  fog  forms  a  relatively  small 
proportion  of  the  total  deposit  usually  referred  to  as  chemical 
fog,  but  this  is  not  known.  The  two  can  not  be  separated.  It 
is  evident  that  the  developer  may  play  a  large  part  in  determin- 
ing to  what  extent  development  of  emulsion  fog  takes  place. 
It  is  possible,  however,  that  in  addition  to  the  reduction  of 
these  previously  nucleated  grains,  new  grains  in  the  emulsion 
are  rendered  developable  by  some  specific  action  of  the  reduc- 
ing solution.  The  term  chemical  fog  is  applied  more  strictly 
to  the  deposit  resulting  from  the  latter  cause. 

Chemical  fog  may  be  produced  by  physical  or  chemical 
development,  and  may  show  differences  from  the  image  in 
structure  and  in  grain  distribution. 

For  the  present,  studies  of  fog  must  be  confined  to  the  total 
effect,  from  whatever  cause.  It  is  pointed  out,  however,  that 

171 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

the  complex  nature  of  the  fog  production  probably  accounts 
for  the  fact  that  the  relations  for  fog  are  different  from  those 
for  the  image. 

Fog  tends  to  a  definite  limit  or  equilibrium  density.  The 
growth  of  fog  with  time  was  found  to  be  described  quite 
accurately  by  the  equation 

D  =  Do,  (1   -  c-*0-W)f  (28) 

where  Deo  is  the  ultimate  or  equilibrium  density  and  /0  the 
time  at  which  fogging  begins.  The  fogging  velocity  is 

™  .K(Da>    -D).  (29) 

Accordingly,  the  growth  of  the  image  and  that  of  the  fog 
do  not  appear  to  follow  the  same  law.  (Compare  equation 
16  and  18  with  28  and  29.)  Equation  28  is  the  first  order 
reaction  law  corrected  for  a  period  of  delay.  It  is  probable 
that  most  of  the  fog  results  from  physical  development  and 
that  the  process  is  therefore  freed  from  some  of  the  restric- 
tions imposed  on  the  development  of  the  image,  where  the 
grains  are  fixed  in  place  and  have  a  definite  distribution,  and 
the  gelatine  plays  a  part.  Fog  does  not  vary  with  reduction 
potential  nor  with  other  common  properties  of  a  developer. 
(See  Chapter  VIII,  Table  36.) 

It  is  difficult  to  find  a  quantitative  expression  for  fogging 
power.  The  best,  and  one  which  indicates  fairly  well  the 
relative  amounts  of  fog  obtained  in  a  definite  time,  is  obtained 
by  using  the  fogging  velocity  at  an  intermediate  time,  such 
as  ten  minutes.  (See  Chapter  VIII,  Tables  35,  36,  37). 

The  character  of  the  possible  action  of  fogging  agents  is 
indicated  by  the  fact  that  with  thiocarbamide  the  developer 
reduces,  in  the  presence  of  the  fogging  agent,  no  more  grains 
than  it  does  alone.  Other  indirect  evidence  indicates  that 
fogging  agents  have  the  power  of  nucleation,  and  that  this 
action  is  increased  by  increased  solubility  of  the  silver  halide. 
The  fogging  agent  may  therefore  be  considered  as  rendering 
developable  and  reducing  grains  which  the  developing  agent 
can  not  effect.  That  this  is  not  a  matter  of  reduction  poten- 
tial is  quite  certain.  The  developing  agent  may  have  the 
same  power  of  nucleation,  which  means  that  very  pure  reduc- 
ing agents  of  low  reduction  potential  may  produce  much  fog. 

The  distribution  of  fog  over  the  image  was  studied  from 
the  standpoint  of  preceding  work,  and  it  was  found  that  fog 
is  practically  absent  from  the  high  densities,  but  increases  as 

172 


THE  THEORY  OF  DEVELOPMENT 

the  image  densities  decrease.  Experimental  data  interpreted 
in  the  light  of  the  general  laws  for  the  growth  of  the  image  and 
the  effect  of  bromide  led  to  the  equation 

F  =  k  (Di   -  DiJ  (30) 

for  the  fog.  A  is  the  density  of  the  image  corresponding  to 
the  fog  F,  and  Dio  is  the  density  required  practically  to  prevent 
fog  (i.  e.,  the  growth  of  this  density  is  rapid  enough  so  that  the 
free  bromide  formed  prevents  fog) .  Equation  30  is  a  straight 
line  of  slope  k,  and  k  is  apparently  equal  to  unity. 

The  fogging  action  of  thiocarbamide  was  studied  and  found 
to  be  apparently  the  same  as  that  of  ordinary  fogging  agents  or 
developers  giving  fog.  Results  obtained  here,  as  well  as  the 
work  on  the  concentration  of  bromide  present  after  develop- 
ment, confirmed  equation  30. 

Direct  and  indirect  evidence  indicates  that  fog  is  more 
restrained  by  bromide  than  is  the  image.  This  indicates  also 
that  most  fogging  agents  are  of  relatively  low  reduction 
potential. 

Further  investigation  by  similar  methods  should  yield 
valuable  results  on  phenomena  of  fundamental  importance. 

DATA  BEARING  ON  CHEMICAL  AND  PHYSICAL  PHENOMENA 
OCCURRING  IN  DEVELOPMENT 

The  effect  of  neutral  salts,  potassium  bromide, 

iodide,  ferrocyanide,  etc. 

From  experiments  with  pyrogallol  and  other  developers  at 
very  high  concentrations  of  bromide  it  was  concluded  that  at 
such  concentrations  bromide  has  a  dual  effect: — 

1.  It  appears  to  act  like  a  fogging  agent  in  that  new  grains 
are  rendered  developable ; 

2.  It  probably  forms  complexes  with  the  silver  bromide, 
giving  new  characteristics  to  the  emulsion. 

The  two  effects  are  no  doubt  related.  That  the  result  is 
not  due  primarily  to  action  on  the  gelatine  is  indicated  by 
the  fact  that  for  the  higher  densities  the  velocity  curve  is  of 
the  normal  shape  and  the  velocity  is  not  greatly  changed. 

The  so-called  "acceleration"  of  development  produced  by 
certain  neutral  salts,  such  as  potassium  iodide,  was  investi- 
gated by  the  usual  methods.  Potassium  iodide  was  especially 
studied,  and  its  effects  were  found  to  be  quite  different  from 
those  of  bromide  or  of  the  other  neutral  salts  used.  (See 
Chapter  IX,  Figs  59  and  60.)  This  is  undoubtedly  due  to  a 
reaction  with  the  silver  halide. 

173 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Acceleration  by  other  neutral  salts  may  be  attributed  to 
effects  on  diffusion  and  to  adsorption  of  the  developer. 

The  period  of  induction  is  shortened  by  these  salts,  but  the 
velocity  beyond  this  period  is  not  greatly  changed  and  the 
maximum  density  is  not  affected. 

All  the  results  described  depend  upon  the  character  of  the 
emulsion  used. 

The  effects  of  changes  in  the  constitution  of  the  developing 
solution  are  detailed  for  hydroquinone,  and  less  extensively 
described  for  monomethylparaminophenol.  The  bearing  of 
these  results  is  indicated. 

RELATIONS  BETWEEN  REDUCTION  POTENTIAL  AND 
PHOTOGRAPHIC  PROPERTIES 

Although  the  present  investigation  offers  more  quantitative 
data  on  both  the  reduction  potentials  and  the  photographic 
properties  of  developers  than  have  hitherto  been  available, 
it  is  still  insufficient  to  permit  the  formulation  of  general  rules. 
With  the  methods  well  in  hand,  it  should  be  possible  to  obtain 
the  information  necessary.  At  present  a  few  relations  which 
appear  well  founded  may  be  emphasized : 

The  degree  to  which  a  developer  is  affected  by  bromide 
depends  on  its  reduction  potential.  If  a  developer  is  of  low 
potential,  a  given  amount  of  bromide  will  have  a  greater 
effect  in  lowering  the  density  than  if  the  developer  has  a  high 
potential.  This  is  exclusive  of  the  effect  of  bromide  on  the  fog 
(if  the  latter  is  appreciable),  which  may  be  an  important 
practical  consideration. 

The  speed  of  an  emulsion  varies  with  the  reducer,  but  this 
is  apparently  no  function  of  the  reduction  potential.  A  care- 
ful study  of  the  data  shows  that  even  if  reducers  of  low  fogging 
power  only  are  considered,  (so  that  the  fog  error  is  minimized), 
the  speed  does  not  vary  with  the  reduction  potential. 

If  high  contrast  is  desired  and  prolonged  development  is 
necessary  to  secure  it,  it  is  desirable  to  use  bromide  to  prevent 
fog.  Under  these  conditions,  a  higher  effective  plate  speed  can 
be  secured  from  a  high  reduction  potential  developer  with  as 
much  bromide  as  may  be  necessary  to  eliminate  fog. 

The  maximum  density  tends  to  increase  with  increasing 
reduction  potential. 

Because  of  the  interrelation  of  speed  and  maximum  density? 
the  maximum  contrast  shows  no  regular  variation  with 
reduction,  potential. 

174 


THE  THEORY  OF  DEVELOPMENT 


TABLE  45 


of  Reduction  Potential  Values 


00-0"     0 

STJ.HC1  NH,,H 


rot.       i.o  7  (?) 


Hucloar 

m«:hylatlo 


Sid* -chain 
•athyL&tlo 


CH3     I  JCH(CHj), 


9+  lower   than  p-a-p 

OH 


•H»SO, 


0 


175 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Apparently  no  relation  exists  between  the  time  of  appear- 
ance of  the  image  and  the  reduction  potential.  ta  is  an  indica- 
tor of  the  diffusion  rate  and  the  reaction  resistance,  neither 
one  of  which  is  necessarily  influenced  by  the  potential. 

No  constant  relation  exists  between  K,  the  velocity  constant, 
and  the  potential.  For  developers  of  practically  the  same 
resistance  factors,  the  velocity  varies  approximately  as  the 
potential — i.  e.,  it  increases  with  increasing  ^Br. 

The  fogging  power  of  developers  is  not  a  function  of  the 
reduction  potential. 

Other  relations  which  form  the  basis  for  the  measurement  of 
reduction  potential  are  not  included  here,  as  they  have  been 
discussed. 

It  is  evident  that  factors  other  than  the  potential  control 
the  developing  properties  of  organic  reducers.  Hence  the 
ordinary  practical  working  properties  of  a  developer  are 
neither  safe  nor  generally  useful  criteria  of  its  relative  energy . 

REDUCTION  POTENTIAL  AND  CHEMICAL  STRUCTURE 

Table  45  gives  the  only  quantitative  measurements  obtained 
on  the  relation  between  structure  and  reduction  potential. 
It  will  be  remembered  that  the  values  given  are  based  on  a 
comparison  of  the  developers  at  the  concentration  M/20, 
with  the  same  concentrations  of  sulphite  and  carbonate 
throughout. 

A  survey  of  the  table  indicates  that  the  effect  on  the 
energy  produced  by  the  various  substitutions,  (mentioned  in 
Chapter  I.,  in  connection  with  the  rules  of  Lumiere  and  of 
Andresen),  is  not  as  readily  predicted  as  these  rules  would 
indicate.  Although  it  will  be  necessary  to  measure  many 
more  compounds  before  generalizations  can  be  made,  certain 
tendencies  are  clear. 

It  is  evident  that  the  aminophenols  are  most  energetic,  the 
hydroxyphenols  next,  and  the  amines  the  least,  the  amount  of 
reactive  energy  depending  on  the  number  and  position  of  the 
active  groups.  It  is  consistently  the  case  where  only  two 
active  groups  are  concerned,  and  if  three  groups  are  concerned 
the  measurements  and  experiments  with  other  compounds 
show  that  a  mixture  of  hydroxyl  and  amino  groups  imparts 
greater  energy  to  the  substance. 

The  introduction  of  a  single  methyl  group  in  the  nucleus  o  * 
in  an  amino-group  increases  the  energy. 

Substitution  of  two  methyl  groups  for  the  hydrogen  of  an 
amino-group  appears  to  be  of  doubtful  advantage  over  the 

176 


THE  THEORY  OF  DEVELOPMENT 

preceding.  Contrary  to  Lumiere,  we  find  dimethylparamino- 
phenol  to  be  a  developer,  and  of  greater  energy  than  para- 
minophenol,  though  lower  than  the  monomethyl  substitution 
compound. 

Nuclear  substitution  of  a  halogen  in  the  hydroxy-phenols 
raises  the  energy. 

The  series  of  substituted  paraminophenols  was  especially 
studied  and  additional  relations  are  shown.  In  addition  to 
those  already  stated  the  following  may  be  given: 

In  the  case  of  nuclear  methylation  (one  methyl  group  only) 
the  energy  is  increased,  but  the  increase  depends  on  which 
position  the  methyl  group  occupies  with  respect  to  the  other 
groups.  (See  paramino-orthocresol  and  paramino-metacresol. 
The  latter  has  undoubtedly  greater  energy.) 

Paraminocarvacrol  has  a  much  lower  potential  than  para- 
minophenol,  which  would  indicate  that  further  methylation 
or  increase  in  the  size  of  the  molecule  in  that  direction  is 
undesirable.  Benzyl  paraminophenol  gives  a  result  which 
may  be  questioned,  and  which  should  therefore  be  studied 
further.  (The  energy  is  lowered  by  the  substitution  of  a 
phenyl  group  in  the  amino  group.) 

Introduction  of  another  amino  group  greatly  increases  the 
energy. 

Chlorination  of  paraminophenol  appears  of  doubtful 
advantage. 

Simultaneous  nuclear  and  side  chain  methylation  (one 
methyl  group  for  each)  appears  to  give  greater  energy  than 
either  substitution  alone. 

Change  to  a  glycine  lowers  the  potential,  as  does  also  the 
introduction  of  a  -CH2OH  group. 

These  results  apply  to  the  groups  only  in  the  positions 
shown.  Present  data  do  not  warrant  further  deductions, 
especially  in  view  of  the  fact  that  the  influence  of  the  position 
of  the  groups  is  not  yet  known. 

Many  fallacies  in  the  published  results  of  previous  investiga- 
tions have  come  to  light  during  the  present  investigation.  It 
is  now  quantitatively  proved  that  while  developers  differ  in 
their  action,  and  some  have  objectionable  features,  there  is  a 
considerable  number  of  developers  which  when  properly  used 
ape  capable  of  giving  identical  results.  It  is  very  often  true 
that  a  greater  change  in  results  may  be  brought  about  by 
altering  the  relative  concentrations  of  the  ingredients  of  the 
developing  solution  than  by  using  a  different  reducing  agent. 

177 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

The  action  of  bromide  has  been  dealt  with  at  length,  and 
some  of  its  practical  applications  have  been  pointed  out.  If 
bromide  is  used  in  accordance  with  the  principles  recorded 
above,  there  is  no  doubt  of  its  being  of  real  advantage  for 
much  photographic  work. 


178 


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PIPER,  C.  W.,  The  application  of  physico-chemical  theories  in  plate  testing 

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REISS,    R.,    Photographischen    Bromsilbertrockenplatte.     (Knapp,    Halle 

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SHEPPARD,  S.  E.,  and  MEES,  C.  E.  K.,  Investigations  on  the  theory  of  the 
photographic  process.     (Longmans,   London,    1907.) 

,  — ., ,  — .,  On  the  development  factor.     Phot.  J.  43:  48.  1903. 

,  — ., ,  — .,  On  the  highest  development  factor  attainable. 

Phot.  J.  43:  199.  1903. 
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— ,   — .,   Exposure  and  development  relatively  considered.     Phot. 
J.  35:  288.  1895. 

— ,  — .,  Light  and  development.     Phot.  J.  51:  320.  1911. 
— ,  — .,  Standard  plates  and  some  causes  of  apparent  alteration  in 
rapidity.     Phot.  J.  35:  118.  1895. 
WATKINS,  A.,  Control  in  development.     Brit.  J.  Phot.  42:  133.  1895. 

,  — .,  Development.     Brit.  J.  Phot.  41:  745.  1894. 

— ,  — .,  Photography,  its  principles  and  applications.  (Van  Nostrand, 
New  York,  1911.) 

,  — .,  Some  developers  compared.     Phot.  J.  40:  221.  1900. 

— ,   — .,  Time  development.     Variation  of  temperature  coefficient 
for  different  plates.     Brit.  J.  Phot.  58:  3.  1911. 


VELOCITY   OF   DEVELOPMENT 

ABEGG,  R.,  Theorie  des  Eisenentwicklers  nach  Luther.     Arch.  wiss.  Phot. 

2:  76.  1900. 

BLOCH,  O.,  Plate  speeds.     Phot.  J.  41:  51.  1917. 
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phys.  Chem.  47:  56.  1904. 
COLSON,  R.,  Einfluss  der  Diffusion  der  Bestandteile  des  Entwicklers  bei 

der  photographischen  Entwicklung.     Arch.  wiss.  Phot.  1:  31.  1899. 
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new   method   of  determination   of  the   sensitiveness  of  photographic 

plates.     J.  Soc.  Chem.  Ind.  9:  455.  1890. 

184 


THE  THEORY  OF  DEVELOPMENT 

LEHMANN,    E.,   Zur  Theorie  der  Tiefenentwicklung.     Phot.    Runds.   50: 

55.  1913. 

LUPPO-CRAMER,  Photographische  Probleme.     (Knapp,  Halle  a.  S.,  1907.) 
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a.  S.,  1899.) 

MEES,  C.  E.  K.,  Time  development.     Phot.  J.  50:  403.   1910. 
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and  experimental  work  with  developers.     Brit.  J.  Phot.  60:  119.  1913. 
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58:  75.  1911. 
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Phot.  2:  9.    1900. 
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photographischen     Entwicklern.     III.     Hydrochinon     als     Induktor. 

Zeits.  Elektrochem.  19:816. 1913. 

SHEPPARD,  S.  E.,  Reversibility  of  photographic  development  and  the  retard- 
ing action  of  soluble  bromides.     J.  Chem.  Soc.  87:  1311.  1905. 
,  — .,  Theory  of  alkaline  development,  with  notes  on  the  affinities 

of  certain  reducing  agents.     J.  Chem.  Soc.  89:  530.  1906. 
,  — .,  and  MEES,  C.  E.  K.,  Investigations  on  the  theory  of  the 

photographic  process.     (Longmans,  London,   1907.) 
,  — ., ,  — .,  On  some  points  in  modern  chemical  theory 

and  their  bearing  on  development.     Phot.  J.  45:  241.  1905. 
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development.     Proc,  Roy.  Soc.  74:  457.  1904. 
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II.     Phot.  J.  45:319.  1905. 

— .,   and   MEYER,   G.,    Chemical  induction  and   photographic 


development.     J.  Amer.  Chem.  Soc.  42:  689.  1920;  Phot.  J.  60:  12. 

1920. 

VANZETTI,  B.  L.,  Diffusion  of  electrolytes.     Chem.  Abst.  9:  406.  1915. 
WILDERMANN,    M.,    Ueber  die   Geschwindigkeit   der   Reaktion  vor   voll- 

standigem  Gleichgewichte  und  vor  dem  Uebergangspunkte,   u.  s.  w. 

Zeits.  physik.  Chem.  30:  341.  1899. 


185 


Index  of  Authors 


ABEGG,  R.,  22,  23 
ANDRESEN,  M.,  16,  18,  175 
ARMSTRONG,  H.  E.,  22 
BANCROFT,  W.  D.,  15 
BLOCK,  O.,  84 
BREDIG,  G.,  15 
COLBY,  79 

DRIFFIELD,  V.  C.,  HURTER,  F.,  and 
— ,  22,  25,  30,  32,  33,  59, 

60,   61,   64,   73,   78,  80,  82,   110, 

141,  162,  165 
EDER,  J.  M.,  14 
FRARY,  F.  C.,  29,  147 

— ,  and  MITCHELL,  147 
— ,  and  NIETZ,  A.  H.,  29,  57 
HURTER,  F.,  and  DRIFFIELD,  V.  C  » 

22,    25,   30,    32,    33,    59,    60,    61, 

64,  73,  78,  80,  82,  110,  141,  162, 

165 

JONES,  L.  A.,  26 
LEUBNER,    A.,    LUTHER,    R.     and 

-,  29,  167 

LUMI^RE,  A.,  16,  18,  175 
LUMI&RE,  L.,  16,  18 
LUPPO-CRAMER,  150,  153 
LUTHER,  R.,  22 

— ,  and  LEUBNER,  A.,  29,  167 
MELLOR,  84 


MEES,  C.  E.  K.,  and  PIPER,  C.  W., 
136,  137,  139 

— ,  and  SHEPPARD,  S.  E.,  26 
— ,     SHEPPARD,     S.     E.,     and 

,  18,  25,  29,  30,  32,  33,  80, 

81,  82,  83,  124,  165,  166 
MEYER,  G.,  SHEPPARD,  S.  E.,  and 

,  77,  153 

MITCHELL,     FRARY,     F.     C.,     and 

— ,  147 

NERNST,  W.,  15,  78,  107 
NIETZ,  A.  H.,  92 

,  FRARY,  F.  C.,  and ,. 

29,  57 

OSTWALD,  W.,  15 

PERLEY,  147 

PIPER,  C.  W.,  MEES,  C.  E.  K.,  and 

— ,  136,  137,  139 
SEYEWETZ,  A.,  16,  18 
SHEPPARD,   S.    E.,    18,    19,    23,    24, 

25,    32,   36,   57,    78,    79,    82,  92, 

126,  150,  166 

,  and  MEES,  C.  E.  K.,   18, 

25,  29,  30,  32,  33,  80,  81,  82,  83, 

124,  165,  166 

— ,  and  MEYER,  G.,  77,  153 
— ,  MEES,  C.  E.  K.,  26 
WATERHOUSE,  J.,  147 
WILSEY,  R.  B.,  92,  125 


186 


Index  of  Subjects 


Abegg's  theory  of  bromide  restraint,  22 

—  plan  for  measuring  reduction  potential,  23 
Alkyl  groups,  substitution  of,  in  developer,  17,  18,  176 
Amino  groups,  substitution  of,  in  developer,  17,  18,  176 
Apparatus  used  in  developing  test  plates,  27,  28 

Bloch's  method  of  solving  velocity  equations,  84 
Bromide,  Abegg's  theory  of  restraining  action  of,  22 

abnormal  effect  of  soluble,  on  developer,  150 

advantages  of,  in  developer  for  speed  determination,  69,  178 

chemical  effects  of,  in  developer,  22,  23,  24 

effect  of  soluble,  on  maximum  contrast,  119,  169 

— ,  on  density,  19,  24,  32-58,  113,  122,  150,  160-164, 

173 

— ,  on  fog,  68,  69,  144,  146,  152,  173 
— ,  on  maximum  density,  113-118,  169 
— ,  on  plate  curves,  39,  40,  160-164 
-  — ,  on  reduction  potential,  109 

— ,  on  time  of  appearance  of  image,  32,  125,  170 

— ,  on  velocity,  112,  113,  124,  126,  130,  169,  170 
— ,  on  velocity  constant,  124,  170 
Bromide  concentration  and  density  depression,  19,  24,  32-58,  122,  160-164, 

I/O 

Bromide  concentration  giving  same  maximum  density  for  different  emul- 
sions, 116-118,  169 

Carbonate,  effect  of  variable  quantities  in  developer,  72,  156,  157 
Chemical  fog,  134,  135,  171 
Contrast,  31 

effect  of  fog  on,  101,  143,  166 
maximum,  determination  of,  100 

— ,  effect  of  bromide  on,  119,  169 

— ,  relation  of,  to  reduction  potential,  102,  109 

— ;  variation  of,  with  developer,  102-109,  168 

Density,  concentration  of  bromide  required  to  give  same  maximum,  for 

different  developers  for  same  emulsion,  116-118,  169 
definition  of,  26 
growth  of,  with  development,  31 

•  — ,  with  exposure,  31 

maximum  -       -  equation,  78,  79,  83,  88,  97,  165 

— •,  variation  with   concentration  of  bromide  in 

developer,  113-118,  169 
— •,  variation  with  developer,  113-118,  169 
— • — • —  — •,  variation  with  exposure,  99 

— ,  variation  with  reduction  potential,  102-105,  167 
measurement  of,  30 

Density  depression,  due  to  bromide,  32,  36,  37,  41,  49,  122,  130,  160-164 
a  measure  of  the  shift  of  the  equilibrium,  122,  170 
method  of  measuring  reduction  potential  by,  19,  24, 

32-58,  160-164 
rate  of,  38,  52,  163 
relation  to  bromide  concentration,  38,  41,  49,  163 

187 


MONOGRAPHS  ON  THE   THEORY  OF  PHOTOGRAPHY 

Developers,  abnormal  effects  of  bromide  in,  150,  173 

classification  of,  according  to  fogging  velocity,  140,  142 

,  according  to  maximum  fog,  142 

,  general,  14 

.structural,  16,  174,  175 

depression  with  different  ,  in  relation  to  bromide 

concentration,  49 
effect  of  changes  in  constitution  of,  72,  155 

carbonate  in,  72,  156,  157 

hydroquinone  in,  72,  156,  157 

neutral  salts  in,  150,  153,  154,  173 

potassium  iodide  in,  153,  173 

sulphite  in,  72,  156,  157,  158,  168 

energy  of,  18,  58,  175 

fogging  velocity  of,  138,  172 

formulae  of,  used  for  test  plates,  28 

induction  period  of,  77 

reduction  potential  of,  15,  19,  22,  32,  54,  58,  175 

,  chemical  theory  of  method  of  deter- 

•  mining,  19 

,  table  of  relative,  56,  58,  175 

relation  of  concentration  of  ingredients  of,  to  speed,  72,  165 
—  -  different  -  -  to  speed,  67,  69,  70,  71,  165 

relation  to  fogging,  68,  140,  141,  172 
structure  of,  and    relation    to    photographic    properties,    16, 

174,  176 
substitution  of  alkyl  groups  in,  17,  18,  176 

— amino  groups  in,  17,  18,  176 

variation  of  maximum  contrast  with,  102-109,  168 

maximum  density  with,  102-109,  167 

Development,  method  of,  for  standard  conditions,  26 

velocity  of,  15,  76 
Dichroic  fog,  136 

Emulsion,  effect  of,  on  value  of  density  depression,  54 

Emulsion  fog,  134,  171 

Emulsions  used  for  experimental  work,  29 

Energy  of  developer,  58,  176 

increase  of,  18,  176 
Exposure  of  photographic  plates  for  quantitative  measurement,  25 

importance    of    method    of,    for    speed 

determination,  59 
variation  of  maximum  density  with,  99 

Fog,  chemical,  134,  135,  171 

dichroic,  136 

distribution  over  image,  69,  141,  144-147,  149,  171 

emulsion,  134,  171 

nature  of,  134-137,  171 

relation  of  bromide  to,  68,  69,  144,  146,  152,  173 

relation  to  reduction  potential,  68,  136,  137,  172 
Fogging  action  of  thiocarbamide,  136,  147,  172 
Fogging  power,  137-141,  171 
Fogging  velocity,  expression  for,  138,  172 

of  different  developers,  140,  141,  142 

Glycine,  effect  of  change  to,  in  developer,  17,  18,  177 

188 


THE  THEORY  OF  DEVELOPMENT 

Hurter  and  Driffield's  method  for  determining  the  speed  of  emulsions,  60 

sensitometric  work,  25,  30,  80 

work  on  velocity,  78,  80,  165 
Hydroquinone,  effect  of  variable  quantities  of,  in  developer,  72,  156,  157 

Induction  period  of  developers,  77,  155 

Latent  image,  development  of,  109,  168 
curve  for,  109-111 

Maximum  contrast,  determination  of,  100 

effect  of  bromide  on,  119,  169 
relation  of,  to  reduction  potential,  102-109 
variation  of,  with  developer,  102-109,  168 
Maximum  density,  equation,  78,  79,  83,  88,  97,  165 

variation  of,  with  concentration  of  bromide  in  devel- 
oper, 113-118,  169 
—       — — — ,  with  exposure,  99 

— ,  with  reduction  potential,  102-109,  167 

Neutral  salts,  effect  of,  in  developer,  150,  154,  173 

Nietz's  equation  for  velocity  of  development,  88,  92,  97,  165 

Potassium  bromide,  abnormal  effect  in  developer,  150,  173 

Potassium  citrate,  effect  in  developer,  154 

Potassium  ferrocyanide,  effect  in  developer,  154 

Potassium  iodide,  effect  in  developer,  153 

Potassium  nitrate,  effect  in  developer,  154 

Potassium  oxalate,  effect  in  developer,  154 

Potassium  sulphate,  effect  in  developer,  154 

Reduction  potential  of  developers,  15,  19,  22,  32,  54,  56,  58,  107,  108,  113* 

175 

Abegg's  plan  for  measuring,  23 
chemical  theory  of  method  of  determining,  19 
definition  of,  15,  19 

determination  of,  by  density  depression  method,  19, 
24,  32,  33-58,  122,  160-164 

,  by  maximum  density  method,  113- 

118,  169 
—  — ,  by  Sheppard's  method,  32 

— ,  by  velocity  method,  107,  108,  168 
effect  of  bromide  on,  109 
relation  to  chemical  structure,  176 
-fog,  68,  136,  137,  172 

maximum  contrast,  102-109 

— —  maximum  density,  102-109,  167 
—  photographic  properties,  174 

speed,  70,  72,  165 

sensitometric  theory  of  determining,  30 
Sheppard's  method  of  measuring,  19,  24,  32 

Sensitometry,  25,  31,  80 

Sensitometric  theory  of  method  of  determining  reduction  potentials,  30 

Sheppard's  method  of  measuring  reduction  potential,  19,  24,  32 

velocity  equation,  78 

Sheppard  and  Mees'  work  on  velocity  of  development,  81,  82,  124,  165 
sensitometric  work,  25,  30,  80 

189 


MONOGRAPHS  ON  THE  THEORY  OF  PHOTOGRAPHY 

Speed  of  emulsions,  59,  164 

definition  of  absolute,  65 

determination  of,  59,  62 

determination  by  Hurter  and  Driffield's  method,  60 

— ,   precision  of  method  of,  73 
effect  of  bromide  on,  68,  165 

—  —  changing    concentration    of    ingredients    of 

developers  on,  72,  165 
— -  —  different  developers  on,  67,  69,  70,  71,  165 

contrast,  64 

— reduction  potential  of  developers,  70,  72,  165 

relation  to  exposure,  59 
variation  with  different  emulsions,  66 
Sulphite,  effect  of  variable  quantities  in  developer,  72,  156,  157,  158,  168 

Thiocarbamide,  fogging  action  of,  136,  147,  172 
Time  of  appearance  of  latent  image,  32 

effect  of  soluble  bromide  on,  32,  125,  170 

Velocity  of  development,  76 

Bloch's  method  of  solving  equations  for,  84 

of  fog,  138,  172 

determination  of,  76,  80 

,   reduction   potential   by,    107, 

108,  168 

effect  of  diffusion  on,  78,  83 

soluble  bromides  on,  113,  124,  126,  130, 

170 

two  successive  reactions  on  (Mellor),  84 

equations,  78,  79,  83,  88,  97,  165 

Nernst's  theory  for  reaction ,  78 

Nietz's  equation  for,  88,  92,  97,  165 

Sheppard's  equation  for,  78 

Wilsey's  equation  for,  92 
Velocity  curves,  depression  of,  130,  170 

effect  of  bromide  concentration  on,  126,  170 

Wilsey's  equation  for  velocity  of  development,  92 


190 


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